统计理论

The Bethe-Hessian matrix, introduced by Saade, Krzakala, and Zdeborov\'a (2014), is a Hermitian matrix designed for applying spectral clustering algorithms to sparse networks. Rather than employing a non-symmetric and high-dimensional…

This note develops a Bernstein estimator for lower-tail Spearman's rho and establishes its strong consistency and asymptotic normality under mild regularity conditions. Smoothing the empirical copula yields a strictly smaller mean squared…

In high-dimensional time series analysis, Gaussian approximation (GA) schemes under various distance measures or on various collections of subsets of the Euclidean space play a fundamental role in a wide range of statistical inference…

Model averaging is an important alternative to model selection with attractive prediction accuracy. However, its application to high-dimensional data remains under-explored. We propose a high-dimensional model averaging method via…

In hypothesis testing problems the property of strict unbiasedness describes whether a test is able to discriminate, in the sense of a difference in power, between any distribution in the null hypothesis space and any distribution in the…

Subsampling algorithms for various parametric regression models with massive data have been extensively investigated in recent years. However, all existing studies on subsampling heavily rely on clean massive data. In practical…

We develop nonparametric regression methods for the case when the true regression function is not necessarily smooth. More specifically, our approach is using the fractional Laplacian and is designed to handle the case when the true…

Distribution regression seeks to estimate the conditional distribution of a multivariate response given a continuous covariate. This approach offers a more complete characterization of dependence than traditional regression methods.…

We propose a two-sample test for covariance matrices in the high-dimensional regime, where the dimension diverges proportionally to the sample size. Our hybrid test combines a Frobenius-norm-based statistic as considered in Li and Chen…

In the present paper, we propose a new rank correlation coefficient $r_n$, which is a sample analogue of the theoretical correlation coefficient $r$, which, in turn, was proposed in the recent work of Stepanov (2025b). We discuss the…

We consider the problem of performing parameter and state inference in a state-space model (SSM) parametrized by a static parameter $\theta$. A popular idea to address this problem consists of incorporating $\theta$ in the state of the…

We provide finite-particle convergence rates for the Stein Variational Gradient Descent (SVGD) algorithm in the Kernelized Stein Discrepancy ($\mathsf{KSD}$) and Wasserstein-2 metrics. Our key insight is that the time derivative of the…

In this paper, we develop the mathematical framework for filtering problems arising from biophysical applications where data is collected from confocal laser scanning microscopy recordings of the space-time evolution of intracellular wave…

Many recent developments in causal inference, and functional estimation problems more generally, have been motivated by the fact that classical one-step (first-order) debiasing methods, or their more recent sample-split double…

Bandeira et al. (2022) introduced the Franz-Parisi (FP) criterion for characterizing the computational hard phases in statistical detection problems. The FP criterion, based on an annealed version of the celebrated Franz-Parisi potential…

Stochastic comparisons of series and parallel systems are important in many areas of engineering, operations research and reliability analysis. These comparisons allow for the evaluation of the performance and reliability of systems under…

This paper investigates the asymptotic properties of quantile regression estimators in linear models, with a particular focus on polynomial regressors and robustness to heavy-tailed noise. Under independent and identically distributed…

Given a sample $X_0,...,X_{n-1}$ from a $d$-dimensional stationary time series $(X_t)_{t \in \mathbb{Z}}$, the most commonly used estimator for the spectral density matrix $F(\theta)$ at a given frequency $\theta \in [0,2\pi)$ is the…

Many flexible families of positive random variables exhibit non-closed forms of the density and distribution functions and this feature is considered unappealing for modelling purposes. However, such families are often characterized by a…

This note extends the results of classical parametric statistics like Fisher and Wilks theorem to modern setups with a high or infinite parameter dimension, limited sample size, and possible model misspecification. We consider a special…