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In this article, we establish a near-optimal convergence rate for the CLT of linear eigenvalue statistics of Wigner matrices, in Kolmogorov-Smirnov distance. For all test functions $f\in C^5(\mathbb R)$, we show that the convergence rate is…

Probability · Mathematics 2021-03-22 Zhigang Bao , Yukun He

We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…

Statistics Theory · Mathematics 2007-12-18 Jiming Jiang , Yihui Luan , You-Gan Wang

In this paper new two-dimensional goodness of fit tests are proposed. They are of supremum-type and are based on different types of characterizations. For the first time a characterization based on independence of two statistics is used for…

Methodology · Statistics 2023-05-30 Bojana Milošević , Marko Obradović

This paper studies the residual empirical process of long- and short-memory time series regression models and establishes its uniform expansion under a general framework. The results are applied to the stochastic regression models and…

Statistics Theory · Mathematics 2012-11-16 Ngai Hang Chan , Shiqing Ling

We consider estimating the transition probability matrix of a finite-state finite-observation alphabet hidden Markov model with known observation probabilities. The main contribution is a two-step algorithm; a method of moments estimator…

Systems and Control · Computer Science 2017-11-22 Robert Mattila , Cristian R. Rojas , Vikram Krishnamurthy , Bo Wahlberg

We study the asymptotic properties of a class of estimators of the structural parameters in dynamic discrete choice games. We consider K-stage policy iteration (PI) estimators, where K denotes the number of policy iterations employed in the…

Econometrics · Economics 2020-05-26 Federico A. Bugni , Jackson Bunting

We investigate the asymptotics of eigenvalues of sample covariance matrices associated with a class of non-independent Gaussian processes (separable and temporally stationary) under the Kolmogorov asymptotic regime. The limiting spectral…

Probability · Mathematics 2019-10-11 Tiebin Mi , Robert Caiming Qiu

This paper develops a new framework for indirect statistical inference with guaranteed necessity and sufficiency, applicable to continuous random variables. We prove that when comparing exponentially transformed order statistics from an…

Statistics Theory · Mathematics 2025-09-25 Z Zhang , X Hu , C Lu , T Liu

The sequential multiple testing problem is considered under two generalized error metrics. Under the first one, the probability of at least $k$ mistakes, of any kind, is controlled. Under the second, the probabilities of at least $k_1$…

Statistics Theory · Mathematics 2019-02-18 Yanglei Song , Georgios Fellouris

We consider a novel multivariate nonparametric two-sample testing problem where, under the alternative, distributions $P$ and $Q$ are separated in an integral probability metric over functions of bounded total variation (TV IPM). We propose…

Statistics Theory · Mathematics 2024-09-25 Alden Green , Sivaraman Balakrishnan , Ryan J. Tibshirani

In the asymptotic theory of quantum hypothesis testing, the minimal error probability of the first kind jumps sharply from zero to one when the error exponent of the second kind passes by the point of the relative entropy of the two states…

Quantum Physics · Physics 2014-02-28 Ke Li

This paper deals with a class of nonparametric two-sample tests for ordered alternatives. The test statistics proposed are based on the number of observations from one sample that precede or exceed a threshold specified by the other sample,…

Statistics Theory · Mathematics 2016-11-01 Eugenia Stoimenova , N. Balakrishnan

In this paper we present results on asymptotic characteristics of multivariate function classes in the uniform norm. Our main interest is the approximation of functions with mixed smoothness parameter not larger than $1/2$. Our focus will…

Functional Analysis · Mathematics 2021-11-01 Vladimir Temlyakov , Tino Ullrich

Let $(X_1,Y_1),\ldots,(X_n,Y_n)$ be an i.i.d. sample from a bivariate distribution function that lies in the max-domain of attraction of an extreme value distribution. The asymptotic joint distribution of the standardized component-wise…

Statistics Theory · Mathematics 2015-04-03 Sami Umut Can , John H. J. Einmahl , Estate V. Khmaladze , Roger J. A. Laeven

This paper is concerned with tests for changes in the jump behaviour of a time-continuous process. Based on results on weak convergence of a sequential empirical tail integral process, asymptotics of certain tests statistics for breaks in…

Methodology · Statistics 2014-12-18 Axel Bücher , Michael Hoffmann , Mathias Vetter , Holger Dette

We study the high-dimensional uniformity testing problem, which involves testing whether the underlying distribution is the uniform distribution, given $n$ data points on the $p$-dimensional unit hypersphere. While this problem has been…

Statistics Theory · Mathematics 2025-06-03 Tiefeng Jiang , Tuan Pham

In this work, we give a novel general approach for distribution testing. We describe two techniques: our first technique gives sample-optimal testers, while our second technique gives matching sample lower bounds. As a consequence, we…

Data Structures and Algorithms · Computer Science 2016-05-10 Ilias Diakonikolas , Daniel M. Kane

We prove that if a rectangular matrix with uniformly small entries and approximately orthogonal rows is applied to the independent standardized random variables with uniformly bounded third moments, then the empirical CDF of the resulting…

Probability · Mathematics 2007-06-14 Bernard Bercu , Wlodzimierz Bryc

We study the problem of space and time efficient evaluation of a nonparametric estimator that approximates an unknown density. In the regime where consistent estimation is possible, we use a piecewise multivariate polynomial interpolation…

Statistics Theory · Mathematics 2020-11-11 Paxton Turner , Jingbo Liu , Philippe Rigollet

In this work, we attempt to refine the classic asymptotic formulae to describe the probability distribution of likelihood-ratio statistical tests. The idea is to split the probability distribution function into two parts. One part is…

Data Analysis, Statistics and Probability · Physics 2025-07-29 Li-Gang Xia , Yan Zhang