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In this work, we revisit the one- and two-sample testing problems: binary hypothesis testing in which one or both distributions are unknown. For the one-sample test, we provide a more streamlined proof of the asymptotic optimality of…

Information Theory · Computer Science 2026-04-21 Arick Grootveld , Biao Chen , Venkata Gandikota

We establish the asymptotic distribution of likelihood ratio tests (LRTs) in settings where some of the nuisance parameters are unidentifiable under the null hypothesis, parameters of interest lie on the boundary of the parameter space, and…

Statistics Theory · Mathematics 2026-05-13 Karl Oskar Ekvall , Ola Hössjer , Matteo Bottai , J. M. Patrik Albin

Consider the likelihood ratio test (LRT) statistics for the independence of sub-vectors from a $p$-variate normal random vector. We are devoted to deriving the limiting distributions of the LRT statistics based on a random sample of size…

Statistics Theory · Mathematics 2022-07-22 Mingyue Hu , Yongcheng Qi

We propose a two-sample extended empirical likelihood for inference on the difference between two p-dimensional parameters defined by estimating equations. The standard two-sample empirical likelihood for the difference is Bartlett…

Statistics Theory · Mathematics 2014-12-24 Min Tsao , Fan Wu

We propose a new asymptotic test for the separability of a covariance matrix. The null distribution is valid in wide matrix elliptical model that includes, in particular, both matrix Gaussian and matrix $t$-distribution. The test is fast to…

Statistics Theory · Mathematics 2026-01-26 Joni Virta , Takeru Matsuda

Over the last several decades, improvements in the fields of analytic combinatorics and computer algebra have made determining the asymptotic behaviour of sequences satisfying linear recurrence relations with polynomial coefficients largely…

Symbolic Computation · Computer Science 2023-06-27 Ruiwen Dong , Stephen Melczer , Marc Mezzarobba

For random samples of size n obtained from p-variate normal distributions, we consider the classical likelihood ratio tests (LRT) for their means and covariance matrices in the high-dimensional setting. These test statistics have been…

Statistics Theory · Mathematics 2013-06-04 Tiefeng Jiang , Fan Yang

Edgeworth expansions of first and second order are established for general linear rank statistics under the null hypothesis with asymptotically ''sufficiently'' small remainder terms. The methods used are the Stein method combined with an…

Statistics Theory · Mathematics 2025-11-18 Walter Schneller

This paper discusses fluctuations of linear spectral statistics of high-dimensional sample covariance matrices when the underlying population follows an elliptical distribution. Such population often possesses high order correlations among…

Statistics Theory · Mathematics 2018-03-22 Jiang Hu , Weiming Li , Zhi Liu , Wang Zhou

In this paper, we propose a new modified likelihood ratio test (LRT) for simultaneously testing mean vectors and covariance matrices of two-sample populations in high-dimensional settings. By employing tools from Random Matrix Theory (RMT),…

Applications · Statistics 2024-03-12 Zhenzhen Niu , Jianghao Li , Wenya Luo , Zhidong Bai

We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…

Machine Learning · Computer Science 2024-12-03 Maryam Aliakbarpour , Piotr Indyk , Ronitt Rubinfeld , Sandeep Silwal

Nonparametric tests for equality of multivariate distributions are frequently desired in research. It is commonly required that test-procedures based on relatively small samples of vectors accurately control the corresponding Type I Error…

Methodology · Statistics 2021-01-14 Ablert Vexler , Gregory Gurevich , Li Zou

Nonparametric two-stage procedures to construct fixed-width confidence intervals are studied to quantify uncertainty. It is shown that the validity of the random central limit theorem (RCLT) accompanied by a consistent and asymptotically…

Statistics Theory · Mathematics 2019-10-08 Yuan-Tsung Chang , Ansgar Steland

We study local asymptotic normality of M-estimates of convex minimization in an infinite dimensional parameter space. The objective function of M-estimates is not necessary differentiable and is possibly subject to convex constraints. In…

Statistics Theory · Mathematics 2017-04-11 Kosaku Takanashi

A test of the null hypothesis that a hazard rate is monotone nondecreasing, versus the alternative that it is not, is proposed. Both the test statistic and the means of calibrating it are new. Unlike previous approaches, neither is based on…

Statistics Theory · Mathematics 2007-06-13 Peter Hall , Ingrid Van Keilegom

The aim of this paper is to study the asymptotic expansion in total variation in the Central Limit Theorem when the law of the basic random variable is locally lower-bounded by the Lebesgue measure (or equivalently, has an absolutely…

Probability · Mathematics 2016-07-18 Vlad Bally , Lucia Caramellino

We establish the validity of the empirical Edgeworth expansion (EE) for a studentized trimmed mean, under the sole condition that the underlying distribution function of the observations satisfies a local smoothness condition near the two…

Statistics Theory · Mathematics 2011-06-28 Nadezhda Gribkova , Roelof Helmers

The density ratio model (DRM) provides a flexible and useful platform for combining information from multiple sources. In this paper, we consider statistical inference under two-sample DRMs with additional parameters defined through and/or…

Statistics Theory · Mathematics 2021-03-01 Meng Yuan , Pengfei Li , Changbao Wu

We develop a nonparametric extension of the sequential generalized likelihood ratio (GLR) test and corresponding time-uniform confidence sequences for the mean of a univariate distribution. By utilizing a geometric interpretation of the GLR…

Statistics Theory · Mathematics 2021-05-17 Jaehyeok Shin , Aaditya Ramdas , Alessandro Rinaldo

Calibration of mean estimates for predictions is a crucial property in many applications, particularly in the fields of financial and actuarial decision-making. In this paper, we first review classical approaches for validating…

Applications · Statistics 2025-10-29 Łukasz Delong , Mario Wüthrich