统计理论

Suppose $\widehat\theta_n$ is a strongly consistent estimator for $\theta_0$ in some i.i.d. situation. Let $N_\varepsilon$ and $Q_\varepsilon$ be respectively the last $n$ and the total number of $n$ for which $\widehat\theta_n$ is at least…

Suppose $\{\widehat\theta_n\colon n\ge1\}$ is a strongly consistent sequence of estimators for a parameter $\theta$, where $\widehat\theta_n$ is based on the first $n$ observations. Consider $Q_\varepsilon$, the number of times…

We propose ULFS-KDPE, a kernel debiased plug-in estimator based on the universal least favorable submodel, for estimating pathwise differentiable parameters in nonparametric models. The method constructs a data-adaptive debiasing flow in a…

Variational inference approximates Bayesian posterior distributions by projecting onto a tractable family of distributions. While most theoretical analyses evaluate the quality of this approximation using global divergence measures, many…

I--MR charts commonly estimate the process standard deviation $\sigma$ via the span-2 average moving range divided by the unbiasing constant $d_2$; unlike the unbiased sample standard deviation ($S/c_4$), this estimator depends on ordering…

E-values and E-processes (nonnegative supermartingales) provide anytime-valid evidence for sequential testing via Ville's inequality, yet their connection to Bayesian reasoning, representational structure, and computational feasibility are…

Statistical data depth plays an important role in the analysis of multivariate data sets. The main outcome is a center-outward ordering of the observations that can be used both to highlight features of the underlying distribution of the…

We derive a vector generalization of the curvature-corrected Cram\'er--Rao bound (CRB) in the nonasymptotic regime using a Hilbert space square-root embedding. Building on previous scalar results, we establish a \emph{directional} curvature…

This work presents a geometric refinement of the classical Cram\'er--Rao bound (CRB) in the non-asymptotic regime by incorporating curvature-aware corrections based on the second fundamental form associated with the statistical model…

Palm distributions play a central role in the study of point processes and their associated summary statistics. In this paper, we characterize the Palm distributions of the superposition of independent point processes, establishing a simple…

We study robust high-dimensional sparse regression under finite-variance heavy-tailed noise, epsilon-contamination, and alpha-mixing dependence via two subsampling estimators: Adaptive Importance Sampling (AIS) and Stratified Sub-sampling…

We consider the problem of sketching set valuation functions, defined as the expectation of a valuation function applied to independent random item values. For valuation functions that are monotone and either subadditive or submodular, and…

We study Bayesian inference of an unknown matching $\pi^*$ between two correlated random point sets $\{X_i\}_{i=1}^n$ and $\{Y_i\}_{i=1}^n$ in $[0,1]^d$, under a critical scaling $\|X_i-Y_{\pi^*(i)}\|_2 \asymp n^{-1/d}$, in both an exact…

We establish the limiting spectral distribution of Kendall's correlation matrices in the moderate high-dimensional regime where the dimension grows slower than the sample size. Our framework allows observations to be independent but not…

We propose a variational framework for analyzing dependence structures of convex compact random sets based on their support functions. The approach relies on the canonical even--odd decomposition on the unit sphere, which separates…

We study identifiability in continuous-time linear stationary stochastic differential equations with known causal structure. Unlike existing approaches, we relax the assumption of a known diffusion matrix, thereby respecting the model's…

We introduce the $W$-footrule coefficient $\Phi_C$, a copula-based coefficient of negative association defined as the $L^1$-distance to the countermonotonic copula $W$. We prove that Gini's gamma admits the decomposition $\gamma_C =…

We derive inferential procedures for large sample sizes that remain valid under data-dependent significance levels (so-called "post-hoc valid inference"). Classical statistical tools require that the significance level -- the "type-I error"…

The problem of nonlinear functional of parameters, such as differential entropy, has received much attention in information theory and statistics. In many situations, prior information about the parameters is available in the form of order…

Restricting statistical experiments via nuisance-ancillary $\sigma$-fields yields nuisance-free experiments. However, a moot point with ancillarity is that maximal ancillary $\sigma$-fields are typically not unique. There are exceptions,…