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We study accuracy of bootstrap procedures for estimation of quantiles of a smooth function of a sum of independent sub-Gaussian random vectors. We establish higher-order approximation bounds with error terms depending on a sample size and a…

Statistics Theory · Mathematics 2020-09-21 Mayya Zhilova

In this article, we obtain explicit bounds on the uniform distance between the cumulative distribution function of a standardized sum $S_n$ of $n$ independent centered random variables with moments of order four and its first-order…

Probability · Mathematics 2025-07-30 Alexis Derumigny , Lucas Girard , Yannick Guyonvarch

We obtain non-uniform Edgeworth expansions for several classes of weakly dependent (non-stationary) sequences of random variables, including uniformly elliptic inhomogeneous Markov chains, random and time-varying (partially) hyperbolic or…

Probability · Mathematics 2025-11-11 Yeor Hafouta

This paper provides a finite sample bound for the error term in the Edgeworth expansion for a sum of independent, potentially discrete, nonlattice random vectors, using a uniform-in-$P$ version of the weaker Cram\'{e}r condition in Angst…

Statistics Theory · Mathematics 2019-08-14 Kyungchul Song

In this paper, we derive higher order Edgeworth expansions for the finite sample distributions of the subsampling-based t-statistic and the Wald statistic in the Gaussian location model under the so-called fixed-smoothing paradigm. In…

Statistics Theory · Mathematics 2013-09-11 Xianyang Zhang , Xiaofeng Shao

Performance accuracy of the Euclidean Distance Discriminant rule (EDDR) is studied in the high-dimensional asymptotic framework which allows the dimensionality to exceed sample size. Under mild assumptions on the traces of the covariance…

Statistics Theory · Mathematics 2014-03-04 H. Watanabe , M. Hyodo , T. Seo , T. Pavlenko

A sum of observations derived by a simple random sampling design from a population of independent random variables is studied. A procedure finding a general term of Edgeworth asymptotic expansion is presented. The Lindeberg condition of…

Statistics Theory · Mathematics 2013-12-12 Ibrahim Bin Mohamed , Sherzod M. Mirakhmedov

The aim of this paper is to discuss both higher-order asymptotic expansions and skewed approximations for the Bayesian Discrepancy Measure for testing precise statistical hypotheses. In particular, we derive results on third-order…

Methodology · Statistics 2025-05-02 Elena Bortolato , Francesco Bertolino , Monica Musio , Laura Ventura

We obtain asymptotic expansions for local probabilities of partial sums for uniformly bounded independent but not necessarily identically distributed integer-valued random variables. The expansions involve products of polynomials and…

Probability · Mathematics 2020-12-02 Dmitry Dolgopyat , Yeor Hafouta

The problem of binary hypothesis testing between two probability measures is considered. New sharp bounds are derived for the best achievable error probability of such tests based on independent and identically distributed observations.…

Information Theory · Computer Science 2024-05-30 Valentinian Lungu , Ioannis Kontoyiannis

We study the distribution of a general class of asymptoticallylinear statistics which are symmetric functions of $N$ independent observations. The distribution functions of these statistics are approximated by an Edgeworth expansion with a…

Statistics Theory · Mathematics 2021-02-09 Friedrich Götze , Mindaugas Bloznelis

This paper deals with the Gaussian and bootstrap approximations to the distribution of the max statistic in high dimensions. This statistic takes the form of the maximum over components of the sum of independent random vectors and its…

Statistics Theory · Mathematics 2022-05-31 Victor Chernozhukov , Denis Chetverikov , Kengo Kato , Yuta Koike

We explore some properties of the conditional distribution of an i.i.d. sample under large exceedances of its sum. Thresholds for the asymptotic independance of the summands are observed, in contrast with the classical case when the…

Statistics Theory · Mathematics 2016-10-14 Maeva Biret , Michel Broniatowski , Zangsheng Cao

Consider $M$-estimation in a semiparametric model that is characterized by a Euclidean parameter of interest and an infinite-dimensional nuisance parameter. As a general purpose approach to statistical inferences, the bootstrap has found…

Statistics Theory · Mathematics 2011-02-04 Guang Cheng , Jianhua Z. Huang

We develop and implement a novel fast bootstrap for dependent data. Our scheme is based on the i.i.d. resampling of the smoothed moment indicators. We characterize the class of parametric and semi-parametric estimation problems for which…

Methodology · Statistics 2022-01-19 Davide La Vecchia , Alban Moor , Olivier Scaillet

Lower and upper bounds are explored for the uniform (Kolmogorov) and $L^2$-distances between the distributions of weighted sums of dependent summands and the normal law. The results are illustrated for several classes of random variables…

Probability · Mathematics 2023-08-08 S. G. Bobkov , G. P. Chistyakov , F. Götze

This paper provides conditions under which subsampling and the bootstrap can be used to construct estimators of the quantiles of the distribution of a root that behave well uniformly over a large class of distributions $\mathbf{P}$. These…

Statistics Theory · Mathematics 2013-02-19 Joseph P. Romano , Azeem M. Shaikh

We generalize the maximum likelihood method to non-Gaussian distribution functions by means of the multivariate Edgeworth expansion. We stress the potential interest of this technique in all those cosmological problems in which the…

Astrophysics · Physics 2007-05-23 Luca Amendola

We derive a Gaussian approximation result for the maximum of a sum of high-dimensional random vectors. Specifically, we establish conditions under which the distribution of the maximum is approximated by that of the maximum of a sum of the…

Statistics Theory · Mathematics 2018-01-24 Victor Chernozhukov , Denis Chetverikov , Kengo Kato

The recent seminal work of Chernozhukov, Chetverikov and Kato has shown that bootstrap approximation for the maximum of a sum of independent random vectors is justified even when the dimension is much larger than the sample size. In this…

Statistics Theory · Mathematics 2026-03-17 Yuta Koike
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