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3,100 | Nonparametric Volatility Density Estimation | math.ST | We consider two kinds of stochastic volatility models. Both kinds of models
contain a stationary volatility process, the density of which, at a fixed
instant in time, we aim to estimate.
We discuss discrete time models where for instance a log price process is
modeled as the product of a volatility process and i.i.d.... | math |
3,101 | Asymptotic accuracy of the jackknife variance estimator for certain smooth statistics | math.ST | We show that that the jackknife variance estimator $v_{jack}$ and the the
infinitesimal jackknife variance estimator are asymptotically equivalent if the
functional of interest is a smooth function of the mean or a smooth trimmed
L-statistic. We calculate the asymptotic variance of $v_{jack}$ for these
functionals. | math |
3,102 | Approximating distribution functions by iterated function systems | math.ST | In this paper an iterated function system on the space of distribution
functions is built. The inverse problem is introduced and studied by convex
optimization problems. Some applications of this method to approximation of
distribution functions and to estimation theory are given. | math |
3,103 | Statistical analysis of stochastic resonance with ergodic diffusion noise | math.ST | A subthreshold signal is transmitted through a channel and may be detected
when some noise -- with known structure and proportional to some level -- is
added to the data. There is an optimal noise level, called stochastic
resonance, that corresponds to the highest Fisher information in the problem of
estimation of the ... | math |
3,104 | Asymptotic normality of kernel type deconvolution estimators | math.ST | We derive asymptotic normality of kernel type deconvolution estimators of the
density, the distribution function at a fixed point, and of the probability of
an interval. We consider the so called super smooth case where the
characteristic function of the known distribution decreases exponentially.
It turns out that t... | math |
3,105 | Annuities under random rates of interest - revisited | math.ST | In the article we consider accumulated values of annuities-certain with
yearly payments with independent random interest rates. We focus on annuities
with payments varying in arithmetic and geometric progression which are
important basic varying annuities (see Kellison, 1991). They appear to be a
generalization of the ... | math |
3,106 | Estimation of Weibull Shape Parameter by Shrinkage Towards an Interval Under Failure Censored Sampling | math.ST | This paper is speculated to propose a class of shrinkage estimators for shape
parameter beta in failure censored samples from two-parameter Weibull
distribution when some 'apriori' or guessed interval containing the parameter
beta is available in addition to sample information and analyses their
properties. Some estima... | math |
3,107 | Estimating a structural distribution function by grouping | math.ST | By the method of Poissonization we confirm some existing results concerning
consistent estimation of the structural distribution function in the situation
of a large number of rare events. Inconsistency of the so called natural
estimator is proved. The method of grouping in cells of equal size is
investigated and its c... | math |
3,108 | An Illuminating Counterexample | math.ST | We give a visually appealing counterexample to the proposition that unbiased
estimators are better than biased estimators. | math |
3,109 | Nonparametric volatility density estimation for discrete time models | math.ST | We consider discrete time models for asset prices with a stationary
volatility process. We aim at estimating the multivariate density of this
process at a set of consecutive time instants. A Fourier type deconvolution
kernel density estimator based on the logarithm of the squared process is
proposed to estimate the vol... | math |
3,110 | On-line tracking of a smooth regression function | math.ST | We construct an on-line estimator with equidistant design for tracking a
smooth function from Stone-Ibragimov-Khasminskii class. This estimator has the
optimal convergence rate of risk to zero in sample size. The procedure for
setting coefficients of the estimator is controlled by a single parameter and
has a simple nu... | math |
3,111 | Estimating the structural distribution function of cell probabilities | math.ST | We consider estimation of the structural distribution function of the cell
probabilities of a multinomial sample in situations where the number of cells
is large. We review the performance of the natural estimator, an estimator
based on grouping the cells and a kernel type estimator. Inconsistency of the
natural estima... | math |
3,112 | Combining kernel estimators in the uniform deconvolution problem | math.ST | We construct a density estimator and an estimator of the distribution
function in the uniform deconvolution model. The estimators are based on
inversion formulas and kernel estimators of the density of the observations and
its derivative. Asymptotic normality and the asymptotic biases are derived. | math |
3,113 | Asymptotic Normality of Nonparametric Kernel Type Deconvolution Density Estimators: crossing the Cauchy boundary | math.ST | We derive asymptotic normality of kernel type deconvolution density
estimators. In particular we consider deconvolution problems where the known
component of the convolution has a symmetric lambda-stable distribution,
0<lambda<= 2. It turns out that the limit behavior changes if the exponent
parameter lambda passes the... | math |
3,114 | Asymptotically efficient estimation of linear functionals in inverse regression models | math.ST | In this paper we will discuss a procedure to improve the usual estimator of a
linear functional of the unknown regression function in inverse nonparametric
regression models. In Klaassen, Lee, and Ruymgaart (2001) it has been proved
that this traditional estimator is not asymptotically efficient (in the sense
of the H\... | math |
3,115 | Emerging applications of geometric multiscale analysis | math.ST | Classical multiscale analysis based on wavelets has a number of successful
applications, e.g. in data compression, fast algorithms, and noise removal.
Wavelets, however, are adapted to point singularities, and many phenomena in
several variables exhibit intermediate-dimensional singularities, such as
edges, filaments, ... | math |
3,116 | Hidden Markov and state space models: asymptotic analysis of exact and approximate methods for prediction, filtering, smoothing and statistical inference | math.ST | State space models have long played an important role in signal processing.
The Gaussian case can be treated algorithmically using the famous Kalman
filter. Similarly since the 1970s there has been extensive application of
Hidden Markov models in speech recognition with prediction being the most
important goal. The bas... | math |
3,117 | Statistical equivalence and stochastic process limit theorems | math.ST | A classical limit theorem of stochastic process theory concerns the sample
cumulative distribution function (CDF) from independent random variables. If
the variables are uniformly distributed then these centered CDFs converge in a
suitable sense to the sample paths of a Brownian Bridge. The so-called
Hungarian construc... | math |
3,118 | Asymptotic equivalence of the jackknife and infinitesimal jackknife variance estimators for some smooth statistics | math.ST | The jackknife variance estimator and the the infinitesimal jackknife variance
estimator are shown to be asymptotically equivalent if the functional of
interest is a smooth function of the mean or a trimmed L-statistic with Hoelder
continuous weight function. | math |
3,119 | Selection Criterion for Log-Linear Models Using Statistical Learning Theory | math.ST | Log-linear models are a well-established method for describing statistical
dependencies among a set of n random variables. The observed frequencies of the
n-tuples are explained by a joint probability such that its logarithm is a sum
of functions, where each function depends on as few variables as possible. We
obtain f... | math |
3,120 | Efficient estimation in the accelerated failure time model under cross sectional sampling | math.ST | Consider estimation of the regression parameter in the accelerated failure
time model, when data are obtained by cross sectional sampling. It is shown
that it is possible under regularity of the model to construct an efficient
estimator of the unknown Euclidean regression parameter if the distribution of
the covariate ... | math |
3,121 | Parametric Estimation of Diffusion Processes Sampled at First Exit Times | math.ST | This paper introduces a family of recursively defined estimators of the
parameters of a diffusion process. We use ideas of stochastic algorithms for
the construction of the estimators. Asymptotic consistency of these estimators
and asymptotic normality of an appropriate normalization are proved. The
results are applied... | math |
3,122 | Rates of convergence for constrained deconvolution problem | math.ST | Let $X$ and $Y$ be two independent identically distributed random variables
with density $p(x)$ and $Z=\alpha X+\beta Y$ for some constants $\alpha>0$ and
$\beta>0$. We consider the problem of estimating $p(x)$ by means of the samples
from the distribution of $Z$. Non-parametric estimator based on the sync kernel
is co... | math |
3,123 | On the largest eigenvalue of Wishart matrices with identity covariance when n, p and p/n tend to infinity | math.ST | Let X be a n*p matrix and l_1 the largest eigenvalue of the covariance matrix
X^{*}*X. The "null case" where X_{i,j} are independent Normal(0,1) is of
particular interest for principal component analysis. For this model, when n, p
tend to infinity and n/p tends to gamma in (0,\infty), it was shown in
Johnstone (2001) t... | math |
3,124 | The marginalization paradox does not imply inconsistency for improper priors | math.ST | The marginalization paradox involves a disagreement between two Bayesians who
use two different procedures for calculating a posterior in the presence of an
improper prior. We show that the argument used to justify the procedure of one
of the Bayesians is inapplicable. There is therefore no reason to expect
agreement, ... | math |
3,125 | Nonparametric Estimation in the Model of Moving Average | math.ST | The subject of robust estimation in time series is widely discussed in
literature. One of the approaches is to use GM-estimation. This method
incorporates a broad class of nonparametric estimators which under suitable
conditions includes estimators robust to outliers in data. For the linear
models the sensitivity of GM... | math |
3,126 | Grade of Membership Analysis: One Possible Approach to Foundations | math.ST | Grade of membership (GoM) analysis was introduced in 1974 as a means of
analyzing multivariate categorical data. Since then, it has been successfully
applied to many problems. The primary goal of GoM analysis is to derive
properties of individuals based on results of multivariate measurements; such
properties are given... | math |
3,127 | The suppport reduction algorithm for computing nonparametric function estimates in mixture models | math.ST | Vertex direction algorithms have been around for a few decades in the
experimental design and mixture models literature. We briefly review this type
of algorithm and describe a new member of the family: the support reduction
algorithm. The support reduction algorithm is applied to the problem of
computing nonparametric... | math |
3,128 | Multiscale likelihood analysis and complexity penalized estimation | math.ST | We describe here a framework for a certain class of multiscale likelihood
factorizations wherein, in analogy to a wavelet decomposition of an L^2
function, a given likelihood function has an alternative representation as a
product of conditional densities reflecting information in both the data and
the parameter vector... | math |
3,129 | Confidence balls in Gaussian regression | math.ST | Starting from the observation of an R^n-Gaussian vector of mean f and
covariance matrix \sigma^2 I_n (I_n is the identity matrix), we propose a
method for building a Euclidean confidence ball around f, with prescribed
probability of coverage. For each n, we describe its nonasymptotic property and
show its optimality wi... | math |
3,130 | Minimax estimation of linear functionals over nonconvex parameter spaces | math.ST | The minimax theory for estimating linear functionals is extended to the case
of a finite union of convex parameter spaces. Upper and lower bounds for the
minimax risk can still be described in terms of a modulus of continuity.
However in contrast to the theory for convex parameter spaces rate optimal
procedures are o... | math |
3,131 | Statistical inference for time-inhomogeneous volatility models | math.ST | This paper offers a new approach for estimating and forecasting the
volatility of financial time series. No assumption is made about the parametric
form of the processes. On the contrary, we only suppose that the volatility can
be approximated by a constant over some interval. In such a framework, the main
problem cons... | math |
3,132 | Estimating invariant laws of linear processes by U-statistics | math.ST | Suppose we observe an invertible linear process with independent mean-zero
innovations and with coefficients depending on a finite-dimensional parameter,
and we want to estimate the expectation of some function under the stationary
distribution of the process. The usual estimator would be the empirical
estimator. It ca... | math |
3,133 | The efficiency of the estimators of the parameters in GARCH processes | math.ST | We propose a class of estimators for the parameters of a GARCH(p,q) sequence.
We show that our estimators are consistent and asymptotically normal under
mild conditions. The quasi-maximum likelihood and the likelihood estimators are
discussed in detail. We show that the maximum likelihood estimator is optimal.
If the... | math |
3,134 | Selecting optimal multistep predictors for autoregressive processes of unknown order | math.ST | We consider the problem of choosing the optimal (in the sense of mean-squared
prediction error) multistep predictor for an autoregressive (AR) process of
finite but unknown order. If a working AR model (which is possibly
misspecified) is adopted for multistep predictions, then two competing types of
multistep predictor... | math |
3,135 | Missing at random, likelihood ignorability and model completeness | math.ST | This paper provides further insight into the key concept of missing at random
(MAR) in incomplete data analysis. Following the usual selection modelling
approach we envisage two models with separable parameters: a model for the
response of interest and a model for the missing data mechanism
(MDM). If the response mod... | math |
3,136 | Information bounds for Cox regression models with missing data | math.ST | We derive information bounds for the regression parameters in Cox models when
data are missing at random. These calculations are of interest for
understanding the behavior of efficient estimation in case-cohort designs, a
type of two-phase design often used in cohort studies. The derivations make use
of key lemmas appe... | math |
3,137 | Finite sample properties of multiple imputation estimators | math.ST | Finite sample properties of multiple imputation estimators under the linear
regression model are studied. The exact bias of the multiple imputation
variance estimator is presented. A method of reducing the bias is presented and
simulation is used to make comparisons. We also show that the suggested method
can be used f... | math |
3,138 | Sufficient burn-in for Gibbs samplers for a hierarchical random effects model | math.ST | We consider Gibbs and block Gibbs samplers for a Bayesian hierarchical
version of the one-way random effects model. Drift and minorization conditions
are established for the underlying Markov chains. The drift and minorization
are used in conjunction with results from J. S. Rosenthal [J. Amer. Statist.
Assoc. 90 (199... | math |
3,139 | Mean squared error of empirical predictor | math.ST | The term ``empirical predictor'' refers to a two-stage predictor of a linear
combination of fixed and random effects. In the first stage, a predictor is
obtained but it involves unknown parameters; thus, in the second stage, the
unknown parameters are replaced by their estimators. In this paper, we consider
mean square... | math |
3,140 | Least Angle Regression | math.ST | The purpose of model selection algorithms such as All Subsets, Forward
Selection and Backward Elimination is to choose a linear model on the basis
of the same set of data to which the model will be applied. Typically we have
available a large collection of possible covariates from which we hope to
select a parsimonio... | math |
3,141 | Training samples in objective Bayesian model selection | math.ST | Central to several objective approaches to Bayesian model selection is the
use of training samples (subsets of the data), so as to allow utilization of
improper objective priors. The most common prescription for choosing training
samples is to choose them to be as small as possible, subject to yielding
proper posterior... | math |
3,142 | Local Whittle estimation in nonstationary and unit root cases | math.ST | Asymptotic properties of the local Whittle estimator in the nonstationary
case (d>{1/2}) are explored. For {1/2}<d\leq 1, the estimator is shown to be
consistent, and its limit distribution and the rate of convergence depend on
the value of d. For d=1, the limit distribution is mixed normal.
For d>1 and when the proc... | math |
3,143 | Discussion of "Least angle regression" by Efron et al | math.ST | Discussion of ``Least angle regression'' by Efron et al. [math.ST/0406456] | math |
3,144 | Optimal predictive model selection | math.ST | Often the goal of model selection is to choose a model for future prediction,
and it is natural to measure the accuracy of a future prediction by squared
error loss. Under the Bayesian approach, it is commonly perceived that the
optimal predictive model is the model with highest posterior probability, but
this is not n... | math |
3,145 | Consistent covariate selection and post model selection inference in semiparametric regression | math.ST | This paper presents a model selection technique of estimation in
semiparametric regression models of the type
Y_i=\beta^{\prime}\underbarX_i+f(T_i)+W_i, i=1,...,n. The parametric and
nonparametric components are estimated simultaneously by this procedure.
Estimation is based on a collection of finite-dimensional models... | math |
3,146 | Nonconcave penalized likelihood with a diverging number of parameters | math.ST | A class of variable selection procedures for parametric models via nonconcave
penalized likelihood was proposed by Fan and Li to simultaneously estimate
parameters and select important variables. They demonstrated that this class of
procedures has an oracle property when the number of parameters is finite.
However, in ... | math |
3,147 | Discussion of "Least angle regression" by Efron et al | math.ST | Discussion of ``Least angle regression'' by Efron et al. [math.ST/0406456] | math |
3,148 | Discussion of "Least angle regression" by Efron et al | math.ST | Discussion of ``Least angle regression'' by Efron et al. [math.ST/0406456] | math |
3,149 | Discussion of "Least angle regression" by Efron et al | math.ST | Discussion of ``Least angle regression'' by Efron et al. [math.ST/0406456] | math |
3,150 | Discussion of "Least angle regression" by Efron et al | math.ST | Discussion of ``Least angle regression'' by Efron et al. [math.ST/0406456] | math |
3,151 | Discussion of "Least angle regression" by Efron et al | math.ST | Discussion of ``Least angle regression'' by Efron et al. [math.ST/0406456] | math |
3,152 | Discussion of "Least angle regression" by Efron et al | math.ST | Discussion of ``Least angle regression'' by Efron et al. [math.ST/0406456] | math |
3,153 | Discussion of "Least angle regression" by Efron et al | math.ST | Discussion of ``Least angle regression'' by Efron et al. [math.ST/0406456] | math |
3,154 | Rejoinder to "Least angle regression" by Efron et al | math.ST | Rejoinder to ``Least angle regression'' by Efron et al. [math.ST/0406456] | math |
3,155 | Martingale transforms goodness-of-fit tests in regression models | math.ST | This paper discusses two goodness-of-fit testing problems. The first problem
pertains to fitting an error distribution to an assumed nonlinear parametric
regression model, while the second pertains to fitting a parametric regression
model when the error distribution is unknown. For the first problem the paper
contains ... | math |
3,156 | A stochastic process approach to false discovery control | math.ST | This paper extends the theory of false discovery rates (FDR) pioneered by
Benjamini and Hochberg [J. Roy. Statist. Soc. Ser. B 57 (1995) 289-300].
We develop a framework in which the False Discovery Proportion (FDP)--the
number of false rejections divided by the number of rejections--is treated as a
stochastic proces... | math |
3,157 | Testing predictor contributions in sufficient dimension reduction | math.ST | We develop tests of the hypothesis of no effect for selected predictors in
regression, without assuming a model for the conditional distribution of the
response given the predictors. Predictor effects need not be limited to the
mean function and smoothing is not required. The general approach is based on
sufficient dim... | math |
3,158 | Density estimation for biased data | math.ST | The concept of biased data is well known and its practical applications range
from social sciences and biology to economics and quality control.
These observations arise when a sampling procedure chooses an observation
with probability that depends on the value of the observation. This is an
interesting sampling proc... | math |
3,159 | Semiparametric density estimation by local L_2-fitting | math.ST | This article examines density estimation by combining a parametric approach
with a nonparametric factor. The plug-in parametric estimator is seen as a
crude estimator of the true density and is adjusted by a nonparametric factor.
The nonparametric factor is derived by a criterion called local
L_2-fitting. A class of ... | math |
3,160 | Empirical-likelihood-based confidence interval for the mean with a heavy-tailed distribution | math.ST | Empirical-likelihood-based confidence intervals for a mean were introduced by
Owen [Biometrika 75 (1988) 237-249], where at least a finite second moment is
required. This excludes some important distributions, for example, those in the
domain of attraction of a stable law with index between 1 and 2. In this
article we ... | math |
3,161 | Bounds on coverage probabilities of the empirical likelihood ratio confidence regions | math.ST | This paper studies the least upper bounds on coverage probabilities of the
empirical likelihood ratio confidence regions based on estimating equations.
The implications of the bounds on empirical likelihood inference are also
discussed. | math |
3,162 | Estimation of fractal dimension for a class of Non-Gaussian stationary processes and fields | math.ST | We present the asymptotic distribution theory for a class of increment-based
estimators of the fractal dimension of a random field of the form g{X(t)},
where g:R\to R is an unknown smooth function and X(t) is a real-valued
stationary Gaussian field on R^d, d=1 or 2, whose covariance function obeys a
power law at the or... | math |
3,163 | The empirical process on Gaussian spherical harmonics | math.ST | We establish weak convergence of the empirical process on the spherical
harmonics of a Gaussian random field in the presence of an unknown angular
power spectrum. This result suggests various Gaussianity tests with an
asymptotic justification. The issue of testing for Gaussianity on isotropic
spherical random fields ha... | math |
3,164 | Monomial ideals and the Scarf complex for coherent systems in reliability theory | math.ST | A certain type of integer grid, called here an echelon grid, is an object
found both in coherent systems whose components have a finite or countable
number of levels and in algebraic geometry. If \alpha=(\alpha_1,...,\alpha_d)
is an integer vector representing the state of a system, then the corresponding
algebraic obj... | math |
3,165 | Optimal change-point estimation from indirect observations | math.ST | We study nonparametric change-point estimation from indirect noisy
observations. Focusing on the white noise convolution model, we consider two
classes of functions that are smooth apart from the change-point. We establish
lower bounds on the minimax risk in estimating the change-point and develop
rate optimal estimati... | math |
3,166 | Discussion on Benford's Law and its Application | math.ST | The probability that a number in many naturally occurring tables of numerical
data has first significant digit $d$ is predicted by Benford's Law ${\rm Prob}
(d) = \log_{10} (1 + {\displaystyle{1\over d}}), d = 1, 2 >..., 9$.
Illustrations of Benford's Law from both theoretical and real-life sources on
both science and ... | math |
3,167 | Some improvements in numerical evaluation of symmetric stable density and its derivatives | math.ST | We propose improvements in numerical evaluation of symmetric stable density
and its partial derivatives with respect to the parameters. They are useful for
more reliable evaluation of maximum likelihood estimator and its standard
error. Numerical values of the Fisher information matrix of symmetric stable
distributions... | math |
3,168 | Mimicking counterfactual outcomes to estimate causal effects | math.ST | In observational studies, treatment may be adapted to covariates at several
times without a fixed protocol, in continuous time. Treatment influences
covariates, which influence treatment, which influences covariates, and so on.
Then even time-dependent Cox-models cannot be used to estimate the net
treatment effect. Str... | math |
3,169 | Estimating the causal effect of a time-varying treatment on time-to-event using structural nested failure time models | math.ST | In this paper we review an approach to estimating the causal effect of a
time-varying treatment on time to some event of interest. This approach is
designed for the situation where the treatment may have been repeatedly adapted
to patient characteristics, which themselves may also be time-dependent. In
this situation t... | math |
3,170 | Estimating marginal survival function by adjusting for dependent censoring using many covariates | math.ST | One goal in survival analysis of right-censored data is to estimate the
marginal survival function in the presence of dependent censoring. When many
auxiliary covariates are sufficient to explain the dependent censoring,
estimation based on either a semiparametric model or a nonparametric model of
the conditional survi... | math |
3,171 | Strong consistency of MLE for finite uniform mixtures when the scale parameters are exponentially small | math.ST | We consider maximum likelihood estimation of finite mixture of uniform
distributions. We prove that maximum likelihood estimator is strongly
consistent, if the scale parameters of the component uniform distributions are
restricted from below by exp(-n^d), 0 < d < 1, where n is the sample size. | math |
3,172 | Causal Inference for Complex Longitudinal Data: The Continuous Time g-Computation Formula | math.ST | I write out and discuss how one might try to prove the continuous time
g-computation formula, in the simplest possible case: treatments (labelled a,
for actions) and covariates (l: longitudinal data) form together a bivariate
counting process. This formula is an important missing ingredient in the
continuous time versi... | math |
3,173 | Sharp optimality for density deconvolution with dominating bias | math.ST | We consider estimation of the common probability density $f$ of i.i.d. random
variables $X_i$ that are observed with an additive i.i.d. noise. We assume that
the unknown density $f$ belongs to a class $\mathcal{A}$ of densities whose
characteristic function is described by the exponent $\exp(-\alpha |u|^r)$ as
$|u|\to ... | math |
3,174 | Densities, spectral densities and modality | math.ST | This paper considers the problem of specifying a simple approximating density
function for a given data set (x_1,...,x_n). Simplicity is measured by the
number of modes but several different definitions of approximation are
introduced. The taut string method is used to control the numbers of modes and
to produce candid... | math |
3,175 | Higher criticism for detecting sparse heterogeneous mixtures | math.ST | Higher criticism, or second-level significance testing, is a
multiple-comparisons concept mentioned in passing by Tukey. It concerns a
situation where there are many independent tests of significance and one is
interested in rejecting the joint null hypothesis. Tukey suggested comparing
the fraction of observed signifi... | math |
3,176 | Breakdown points for maximum likelihood estimators of location-scale mixtures | math.ST | ML-estimation based on mixtures of Normal distributions is a widely used tool
for cluster analysis. However, a single outlier can make the parameter
estimation of at least one of the mixture components break down. Among others,
the estimation of mixtures of t-distributions by McLachlan and
Peel [Finite Mixture Models... | math |
3,177 | Asymptotic global robustness in bayesian decision theory | math.ST | In Bayesian decision theory, it is known that robustness with respect to the
loss and the prior can be improved by adding new observations. In this article
we study the rate of robustness improvement with respect to the number of
observations n. Three usual measures of posterior global robustness are
considered: the (r... | math |
3,178 | Game theory, maximum entropy, minimum discrepancy and robust Bayesian decision theory | math.ST | We describe and develop a close relationship between two problems that have
customarily been regarded as distinct: that of maximizing entropy, and that of
minimizing worst-case expected loss. Using a formulation grounded in the
equilibrium theory of zero-sum games between Decision Maker and
Nature, these two problems... | math |
3,179 | Uniform asymptotics for robust location estimates when the scale is unknown | math.ST | Most asymptotic results for robust estimates rely on regularity conditions
that are difficult to verify in practice. Moreover, these results apply to
fixed distribution functions. In the robustness context the distribution of the
data remains largely unspecified and hence results that hold uniformly over a
set of possi... | math |
3,180 | Robust Inference for Univariate Proportional Hazards Frailty Regression Models | math.ST | We consider a class of semiparametric regression models which are
one-parameter extensions of the Cox [J. Roy. Statist. Soc. Ser. B 34 (1972)
187-220] model for right-censored univariate failure times. These models assume
that the hazard given the covariates and a random frailty unique to each
individual has the propor... | math |
3,181 | A Bernstein-von Mises theorem in the nonparametric right-censoring model | math.ST | In the recent Bayesian nonparametric literature, many examples have been
reported in which Bayesian estimators and posterior distributions do not
achieve the optimal convergence rate, indicating that the Bernstein-von
Mises theorem does not hold. In this article, we give a positive result in
this direction by showing... | math |
3,182 | Statistical estimation in the proportional hazards model with risk set sampling | math.ST | Thomas' partial likelihood estimator of regression parameters is widely used
in the analysis of nested case-control data with Cox's model. This paper
proposes a new estimator of the regression parameters, which is consistent and
asymptotically normal. Its asymptotic variance is smaller than that of Thomas'
estimator aw... | math |
3,183 | Convergence rates for posterior distributions and adaptive estimation | math.ST | The goal of this paper is to provide theorems on convergence rates of
posterior distributions that can be applied to obtain good convergence rates in
the context of density estimation as well as regression. We show how to choose
priors so that the posterior distributions converge at the optimal rate without
prior knowl... | math |
3,184 | Needles and straw in haystacks: Empirical Bayes estimates of possibly sparse sequences | math.ST | An empirical Bayes approach to the estimation of possibly sparse sequences
observed in Gaussian white noise is set out and investigated. The prior
considered is a mixture of an atom of probability at zero and a heavy-tailed
density \gamma, with the mixing weight chosen by marginal maximum likelihood,
in the hope of ada... | math |
3,185 | Optimality of neighbor-balanced designs for total effects | math.ST | The purpose of this paper is to study optimality of circular
neighbor-balanced block designs when neighbor effects are present in the model.
In the literature many optimality results are established for direct effects
and neighbor effects separately, but few for total effects, that is, the sum of
direct effect of treat... | math |
3,186 | Construction of E(s^2)-optimal supersaturated designs | math.ST | Booth and Cox proposed the E(s^2) criterion for constructing two-level
supersaturated designs. Nguyen [Technometrics 38 (1996) 69-73] and Tang and Wu
[Canad. J. Statist 25 (1997) 191-201] independently derived a lower bound for
E(s^2). This lower bound can be achieved only when m is a multiple of N-1,
where m is the nu... | math |
3,187 | Complexity regularization via localized random penalties | math.ST | In this article, model selection via penalized empirical loss minimization in
nonparametric classification problems is studied. Data-dependent penalties are
constructed, which are based on estimates of the complexity of a small subclass
of each model class, containing only those functions with small empirical loss.
The... | math |
3,188 | Generalization bounds for averaged classifiers | math.ST | We study a simple learning algorithm for binary classification. Instead of
predicting with the best hypothesis in the hypothesis class, that is, the
hypothesis that minimizes the training error, our algorithm predicts with a
weighted average of all hypotheses, weighted exponentially with respect to
their training error... | math |
3,189 | Statistical properties of the method of regularization with periodic Gaussian reproducing kernel | math.ST | The method of regularization with the Gaussian reproducing kernel is popular
in the machine learning literature and successful in many practical
applications.
In this paper we consider the periodic version of the Gaussian kernel
regularization.
We show in the white noise model setting, that in function spaces of ve... | math |
3,190 | Simultaneous prediction of independent Poisson observables | math.ST | Simultaneous predictive distributions for independent Poisson observables are
investigated. A class of improper prior distributions for Poisson means is
introduced. The Bayesian predictive distributions based on priors from the
introduced class are shown to be admissible under the Kullback-Leibler loss. A
Bayesian pred... | math |
3,191 | Maximum Fisher information in mixed state quantum systems | math.ST | We deal with the maximization of classical Fisher information in a quantum
system depending on an unknown parameter. This problem has been raised by
physicists, who defined [Helstrom (1967) Phys. Lett. A 25 101-102] a quantum
counterpart of classical Fisher information, which has been found to constitute
an upper bound... | math |
3,192 | Aggregation for Regression Learning | math.ST | This paper studies statistical aggregation procedures in regression setting.
A motivating factor is the existence of many different methods of estimation,
leading to possibly competing estimators.
We consider here three different types of aggregation: model selection (MS)
aggregation, convex (C) aggregation and linea... | math |
3,193 | Statistical modeling of causal effects in continuous time | math.ST | This article studies the estimation of the causal effect of a time-varying
treatment on time-to-an-event or on some other continuously distributed
outcome. The paper applies to the situation where treatment is repeatedly
adapted to time-dependent patient characteristics. The treatment effect cannot
be estimated by simp... | math |
3,194 | An introduction to (smoothing spline) ANOVA models in RKHS with examples in geographical data, medicine, atmospheric science and machine learning | math.ST | Smoothing Spline ANOVA (SS-ANOVA) models in reproducing kernel Hilbert spaces
(RKHS) provide a very general framework for data analysis, modeling and
learning in a variety of fields. Discrete, noisy scattered, direct and indirect
observations can be accommodated with multiple inputs and multiple possibly
correlated out... | math |
3,195 | You Can Fool Some People Sometimes | math.ST | We develop an empirical procedure to qunatify future company performance
based on top management promises. We find that the number of future tense
sentence occurrences in 10-K reports is significantly negatively correlated
with the return as well as with the excess return on the company stock price.
We extrapolate the ... | math |
3,196 | A hierarchical technique for estimating location parameter in the presence of missing data | math.ST | This paper proposes a hierarchical method for estimating the location
parameters of a multivariate vector in the presence of missing data. At i th
step of this procedure an estimate of the location parameters for non-missing
components of the vector is based on combining the information in the subset of
observations wi... | math |
3,197 | Dynamics of Interest Rate Curve by Functional Auto-Regression | math.ST | The paper uses functional auto-regression to predict the dynamics of interest
rate curve. It estimates the auto-regressive operator by extending methods of
the reduced-rank auto-regression to the functional data. Such an estimation
technique is better suited for prediction purposes as opposed to the methods
based eithe... | math |
3,198 | Average treatment effect estimation via random recursive partitioning | math.ST | A new matching method is proposed for the estimation of the average treatment
effect of social policy interventions (e.g., training programs or health care
measures). Given an outcome variable, a treatment and a set of pre-treatment
covariates, the method is based on the examination of random recursive
partitions of th... | math |
3,199 | Limiting Behaviour of the Mean Residual Life | math.ST | In survival or reliability studies, the mean residual life or life expectancy
is an important characteristic of the model. Here, we study the limiting
behaviour of the mean residual life, and derive an asymptotic expansion which
can be used to obtain a good approximation for large values of the time
variable. The asymp... | math |
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