统计理论

We propose using a modified conductance-based method to study the mixing time of an important class of two-block Gibbs samplers, the data augmentation (DA) algorithm. %, which is of prominent interest in both theoretical and empirical…

The problem of detecting fake data inspires the following seemingly simple mathematical question. Sample a data point $X$ from the standard normal distribution in $\mathbb{R}^n$. An adversary observes $X$ and corrupts it by adding a vector…

This work makes two advances in the study of the (approximate) nonparametric maximum likelihood estimator (NPMLE) for exponential family mixture models. First, we develop a data-compression strategy that reduces the cost of repeated…

This article discusses the application of stochastic intervention to find the optimal treatment distribution yielding a high value of expected potential outcome under the setting where the number of treatments is allowed to vary with $n$.…

Recent empirical observations suggest that network transitivity is highly correlated with community structure in many real-world networks. In this paper, we theoretically investigate this relationship by deriving the limits of the global…

This paper introduces the separable covariance mixture model, which assumes a data-matrix $Y$ to be of the form $$ \sum\limits_{r=1}^R A_r X B_r $$ for one random $(d \times n)$-matrix $X$ with independent centered variance-one entries, and…

In the context of selective inference, confidence envelopes for the false discoveries allow the user to select any subset of null hypotheses while having a statistical guarantee on the number of false discoveries in the selected set. Many…

A Dirichlet-kernel Gasser-M\"uller (D-GM) estimator is introduced for fixed design regression on the simplex, extending the univariate analog due to Chen [Statist. Sinica, vol. 10(1) (2000), pp. 73-91]. Its pointwise bias and variance,…

Objective functions based on Hellinger distance yield robust and efficient estimators of model parameters. Motivated by privacy and regulatory requirements encountered in contemporary applications, we derive in this paper \emph{private…

This paper studies a specific class of statistical divergences for spectral densities of time series: the spectral $\alpha$-R\'{e}nyi divergences, which include the Itakura-Saito divergence as a limiting case. The aim of this paper is to…

Conformal prediction provides finite-sample, distribution-free coverage under exchangeability, but standard constructions may lack robustness in the presence of outliers or heavy tails. We propose a robust conformal method based on a…

The first passage time problem is considered for stochastic logistic growth model with constant harvesting and multiplicative environmental noise. Explicit expressions for the moments and cumulants of both upcrossing and downcrossing FPTs…

This paper provides an overview of recent developments in quickest change detection (QCD) for high-dimensional multi-sensor systems, with an emphasis on settings involving structural constraints and limited sensing resources. Classical QCD…

In this paper, we study the stability of the shadow, a projection of a measure onto the set of couplings with respect to the Wasserstein distance. The shadow was introduced by \citet{Eckstein_Nutz_2022} to analyze the stability of the…

In this paper, we survey results on the asymptotic behavior of the variance of the best linear unbiased estimator (BLUE) for the mean of stationary processes. This behavior is influenced by the regularity and memory structures of the…

We introduce joint exclusivity (JE), a form of extremal negative dependence that extends the classical notion of mutual exclusivity. The JE structure is analytically tractable and is defined by the exclusion of the interior of the…

The low-degree polynomial framework has emerged as a powerful tool for providing evidence of statistical-computational gaps in high-dimensional inference. For detection problems, the standard approach bounds the low-degree advantage through…

Double/debiased machine learning (DML) provides a general framework for inference with high-dimensional or otherwise complex nuisance parameters by combining Neyman-orthogonal scores with cross-fitting, thereby circumventing classical…

In this paper, we develop a finite mixture of convolutional distributions, a statistical model to analyze continuous data distributed approximately on a mixture of low-dimensional affine subspaces. The observations are assumed independent…

A family of random probabilities is defined and studied. This family contains the Dirichlet process as a special case, corresponding to an inner point in the appropriate parameter space. The extension makes it possible to have random means…