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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