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http://arxiv.org/abs/2404.18256v2
(EIFs) Under Assumptions \ref{assum:consistency}--\ref{assum:observed_data}, the EIFs of $\theta_C(a,a^*)$ and $\theta_I(a,a^*)$ are $\mathcal{D}_{\theta_C(a,a^*)}(\bco) = \psi_{\theta}(a,a^*;\bco) - \theta_C(a,a^*)$ and $\mathcal{D}_{\theta_I(a,a^*)}(\bco) = \frac{N}{\E[N]}\left\{\ps... | 0v01111/StatEval-Statistical-Research |
http://arxiv.org/abs/2504.15879v1
Let $\{N^{(i)}\}_{i = 1}^n$ be a set of i.i.d.~inhomogeneous Poisson point processes, with intensity function $\lambda^*$. Let $\widehat{\lambda}_{\mathrm{Tensor}}$ be the tensor-based estimator output by \Cref{alg1} with the target Tucker rank $(R_1, \dots, R_s)$, and set
\begin... | 0v01111/StatEval-Statistical-Research |
http://arxiv.org/abs/2407.20073v2
Suppose that Assumptions \ref{assum:1}--\ref{assum:rate} hold and both the target domain distribution and tuning samples distribution \(\mathbb{P}\uz,\PP^\dagger \in \PP^{\operatorname{con}}(s^*)\) with any \(s^* \in [0,1]\). Then we have
\begin{equation}
\| \ours (\widehat{\smax}) - ... | 0v01111/StatEval-Statistical-Research |
http://arxiv.org/abs/2404.18256v2
(Nonparametric identification) Under Assumptions \ref{assum:consistency}--\ref{assum:observed_data}, we can identify
\begin{align*}
\theta_C(a,a^*) & = \E\left[\frac{1}{N}\sum_{j=1}^{N}\int_{\bmm} \eta_{\cdot j}(a,\bmm,\bcc,N)\kappa(a^*,\bmm,\bcc,N) \differential \bmm \right],\\
\the... | 0v01111/StatEval-Statistical-Research |
http://arxiv.org/abs/2504.15879v1
Let $\{N^{(i)}\}_{i = 1}^n$ be i.i.d.~inhomogeneous Poisson point processes with intensity function $\lambda^*$. Let $\widehat{\lambda}_{\mathrm{Matrix}}$ be the matrix-based estimator output by \Cref{alg0}, and set
\begin{equation}\label{eq:choice_matrix}
m = \lceil(\|\lambda^*\|_{... | 0v01111/StatEval-Statistical-Research |
http://arxiv.org/abs/2412.10683v2
[The posterior expected empirical divergence converges at a rate $r_{m,n} \lor n^{-1}$]
Let \Cref{assumption-AN,assumption-semimetric,assumption-rate} be satisfied. As $m,n \to \infty$ with $\frac{n}{n+ m} \to c \in (0, 1)$, $ \E{\param}{\diverge_{m,n}(\p_\theta, \p_0) \mid x_{1:n}... | 0v01111/StatEval-Statistical-Research |
http://arxiv.org/abs/2410.12201v2
Suppose \eqref{eq:miscoverage} holds with $\alpha_\ell=\alpha$ for all $\ell\in [L]$, and $\cC_{\ell,\alpha}$'s are independent and identically distributed. Let $\bar{p}(y)= \inf \{ \alpha \in (0, 1) : \pb(y) \in R_\alpha \}$ for each $y\in\cY$, where $R_\alpha$ is defined in \eqref{e... | 0v01111/StatEval-Statistical-Research |
http://arxiv.org/abs/2503.06864v1
[Identification under tilting sensitivity models]
Under Assumptions 1 and 2 in Table \ref{tab:Key-assumptions}, and Model \ref{assump:tilting-MNAR} with fixed $\gamma_{R_{0}}$,
$\gamma_{R_{1}}$ and $\gamma_{S}$, the following identification formula holds for
$\tau$
\begin{align*}
\t... | 0v01111/StatEval-Statistical-Research |
http://arxiv.org/abs/2506.14329v1
Suppose the pre-trained representation is $P$-valid, \cref{ass:A3} holds, and the outcome regression and propensity score
functions $g$ and $m$ satisfy \cref{ass:A1} with constraints $\Pcal_g \cup (s_\psi, d_{\Mcal})$ and $\Pcal_m \cup (s_\psi', d_\Mcal)$, respectively.
Supp... | 0v01111/StatEval-Statistical-Research |
http://arxiv.org/abs/2503.06864v1
Under the assumptions in
Theorem \ref{thm:EIF-tilting} and other regularity conditions in
Assumption \ref{assump:regularity}, we have
\begin{align*}
\widehat{\tau}^{t} & =\frac{1}{N_{\mathcal{R}}}\sum_{i\in\mathcal{R}}R_{i}Y_{i}+\frac{1}{N_{\mathcal{R}}}\sum_{i\in\mathcal{R}}\left[(1... | 0v01111/StatEval-Statistical-Research |
http://arxiv.org/abs/2410.13495v1
Let $X$ be a random element taking values in ${\mathcal B}$ with probability distribution $\P$ fulfilling \ref{itm:Geo} and \ref{itm:Int}. We consider the sequence $(K_n)$ (for $n\in\mathbb{N}$), where $K_n\in \mathcal{S}_{\mathbb{P}_n}(k)$ is a $k$-mean set of the empirical measure ... | 0v01111/StatEval-Statistical-Research |
http://arxiv.org/abs/2404.18256v2
(Efficiency with machine learning estimators) Suppose that Assumptions \ref{assum:consistency}--\ref{assum:observed_data} hold for estimation of $\theta_V(a,a^*)$ ($V\in\{I,C\}$), Assumptions \ref{assum:consistency}--\ref{assum:no_icc} hold for estimation of $\tau_V$, and the nuisance... | 0v01111/StatEval-Statistical-Research |
http://arxiv.org/abs/2503.06864v1
Under the assumptions in Table
\ref{tab:Key-assumptions}, $\tau$ is identifiable by
\begin{enumerate}
\item [(a)] trial participation propensity and outcome means:
$$
\tau=\frac{\E\{\pi_{S}(X)\mu_{1}(X)-\pi_{S}(X)\mu_{0}(X)\}}{P(S=1)}.
$$
\item [(b)] trial participation propensity a... | 0v01111/StatEval-Statistical-Research |
http://arxiv.org/abs/2506.14329v1
Suppose \cref{ass:A1} and \cref{ass:A2} hold. There are sequences $L_n, \nu_n$ and a corresponding sequence of neural network architectures $\Fcal(L_n, \nu_n)$ such that (up to $\log n$ factors)
\begin{align*}
\| \hat f- f_0 \|_{L_2(P_Z)} = O_p\left(\max_{(s, p) \in \Pcal \cup (s_... | 0v01111/StatEval-Statistical-Research |
http://arxiv.org/abs/2404.15060v2
Assume that, for every $n \in \{1, 2, \dots\}$, $Y$ satisfies
\eqref{eq:one_varcomp} with an $X$ with full column rank and parameters
$(\beta_n, h^2_n, \sigma^2_{n})$. If (i) $\lim_{n\to \infty} p_n/n = 0$; (ii$^*$) $\limsup_{n\to\infty}\lambda_{n1} < \infty $; (iii$^*$) $\lim... | 0v01111/StatEval-Statistical-Research |
http://arxiv.org/abs/2503.06864v1
Under Assumptions 1 and 2 in Table \ref{tab:Key-assumptions}, and Model \ref{assump:tilting-MNAR-reduced} with fixed
$\gamma_{R_{0}}$ and $\gamma_{S}$, the following identification
formula and EIF holds for $\tau$:
\[
\tau=\frac{1}{P(S=1)}\E\left\{ \pi_{S}(X)\pi_{R_{1}}(X)\mu_{1}(X)-\... | 0v01111/StatEval-Statistical-Research |
http://arxiv.org/abs/2506.08259v1
The NTUB and SUB unbiasedness thresholds for the null hypothesis $\Po = \{ \bs{\pi} \in \Delta_{pq-1}: \bs{\pi} \; \mathrm{has \; rank \; less \; than } \; r \}$ on the space of $p \times q$ dimensional contingency tables is equal to $2r$. When $n = 2r$ one such SUB power polynomial h... | 0v01111/StatEval-Statistical-Research |
http://arxiv.org/abs/2506.08259v1
Suppose that $\Po$ is algebraic, $\overline{\text{int}(\tilde{\Delta}_{k-1}) \cap \Po} = \Po$, $I_{\mb{R}^{k-1}}(\Po) = \langle f_{(1)},\ldots,f_{(m)} \rangle$, and the matrix $[\nabla f_{(1)} \cdots \nabla f_{(m)}] \in \mb{R}^{k-1 \times m}$ has rank $m$ on $\Po$, then every NTUB tes... | 0v01111/StatEval-Statistical-Research |
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