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We investigate the asymptotic distributions of coordinates of regression M-estimates in the moderate $p/n$ regime, where the number of covariates $p$ grows proportionally with the sample size $n$. Under appropriate regularity conditions, we…

Statistics Theory · Mathematics 2016-12-20 Lihua Lei , Peter J. Bickel , Noureddine El Karoui

Functionals in geometric probability are often expressed as sums of bounded functions exhibiting exponential stabilization. Methods based on cumulant techniques and exponential modifications of measures show that such functionals satisfy…

Probability · Mathematics 2009-09-29 Yu Baryshnikov , P. Eichelsbacher , T. Schreiber , J. E. Yukich

In this article, we obtain a super-exponential rate of convergence in total variation between the traces of the first $m$ powers of an $n\times n$ random unitary matrices and a $2m$-dimensional Gaussian random variable. This generalizes…

Probability · Mathematics 2020-02-06 Kurt Johansson , Gaultier Lambert

In this work, we discuss new bounds for the normal approximation of multivariate Poisson functionals under minimal moment assumptions. Such bounds require one to estimate moments of so-called add-one costs of the functional. Previous works…

Probability · Mathematics 2024-09-05 Tara Trauthwein

This article derives quantitative limit theorems for multivariate Poisson and Poisson process approximations. Employing the solution of Stein's equation for Poisson random variables, we obtain an explicit bound for the multivariate Poisson…

Probability · Mathematics 2021-06-01 Federico Pianoforte , Riccardo Turin

We study the normal approximation of functionals of Poisson measures having the form of a finite sum of multiple integrals. When the integrands are nonnegative, our results yield necessary and sufficient conditions for central limit…

Probability · Mathematics 2012-06-26 Raphael Lachieze-Rey , Giovanni Peccati

This paper considers regularizing a covariance matrix of $p$ variables estimated from $n$ observations, by hard thresholding. We show that the thresholded estimate is consistent in the operator norm as long as the true covariance matrix is…

Statistics Theory · Mathematics 2009-01-21 Peter J. Bickel , Elizaveta Levina

In this paper, we introduce a class of improved estimators for the mean parameter matrix of a multivariate normal distribution with an unknown variance-covariance matrix. In particular, the main results of [D.Ch\'etelat and M. T.…

Statistics Theory · Mathematics 2024-06-25 Arash A. Foroushani , Severien Nkurunziza

This paper aims to examine the characteristics of the posterior distribution of covariance/precision matrices in a "large $p$, large $n$" scenario, where $p$ represents the number of variables and $n$ is the sample size. Our analysis…

Statistics Theory · Mathematics 2026-02-02 Partha Sarkar , Kshitij Khare , Malay Ghosh , Matt P. Wand

Estimating covariance matrices is a problem of fundamental importance in multivariate statistics. In practice it is increasingly frequent to work with data matrices $X$ of dimension $n\times p$, where $p$ and $n$ are both large. Results…

Statistics Theory · Mathematics 2009-01-22 Noureddine El Karoui

Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…

Statistics Theory · Mathematics 2011-12-01 Parikshit Shah , Venkat Chandrasekaran

We study shrinkage estimation of the mean parameters of a class of multivariate distributions for which the diagonal entries of the corresponding covariance matrix are certain quadratic functions of the mean parameter. This class of…

Statistics Theory · Mathematics 2022-07-04 Nikolas Siapoutis , Donald Richards , Bharath K. Sriperumbudur

We first establish strong convergence rates for multiscale systems driven by $\alpha$-stable processes, with analyses constructed in two distinct scaling regimes. When addressing weak convergence rates of this system, we derive four…

Probability · Mathematics 2026-03-03 Kun Yin

Conditional stability estimates require additional regularization for obtaining stable approximate solutions if the validity area of such estimates is not completely known. In this context, we consider ill-posed nonlinear inverse problems…

Numerical Analysis · Mathematics 2020-01-29 Frank Werner , Bernd Hofmann

In this paper we prove discrete to continuum convergence rates for Poisson Learning, a graph-based semi-supervised learning algorithm that is based on solving the graph Poisson equation with a source term consisting of a linear combination…

Analysis of PDEs · Mathematics 2024-07-10 Leon Bungert , Jeff Calder , Max Mihailescu , Kodjo Houssou , Amber Yuan

This paper derives normal approximation results for subgraph counts written as multiparameter stochastic integrals in a random-connection model based on a Poisson point process. By combinatorial arguments we express the cumulants of general…

Probability · Mathematics 2025-11-11 Qingwei Liu , Nicolas Privault

Estimation of the mean and covariance parameters for functional data is a critical task, with local linear smoothing being a popular choice. In recent years, many scientific domains are producing multivariate functional data for which $p$,…

Statistics Theory · Mathematics 2024-09-24 Alexander Petersen

We use a functional analogue of the quantile function for probability measures on $\mathbb{R}^d$ to characterize a novel limit Poisson point process for radially recentred and rescaled random vectors under a radial-directional…

Methodology · Statistics 2025-01-31 Ioannis Papastathopoulos , Lambert de Monte , Ryan Campbell , Haavard Rue

Estimating some mathematical expectations from partially observed data and in particular missing outcomes is a central problem encountered in numerous fields such as transfer learning, counterfactual analysis or causal inference. Matching…

Statistics Theory · Mathematics 2025-05-01 Simon Viel , Lionel Truquet , Ikko Yamane

Quantitative multivariate central limit theorems for general functionals of possibly non-symmetric and non-homogeneous infinite Rademacher sequences are proved by combining discrete Malliavin calculus with the smart path method for normal…

Probability · Mathematics 2017-11-06 Kai Krokowski , Christoph Thaele