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Related papers: Tests for the mean of high-dimensional data

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In this paper, we consider the problem of testing the mean vector in the high dimensional settings. We proposed a new robust scalar transform invariant test based on spatial sign. The proposed test statistic is asymptotically normal under…

Methodology · Statistics 2015-06-30 Long Feng , Fasheng Sun

Change point tests for abrupt changes in the mean of functional data, i.e., random elements in infinite-dimensional Hilbert spaces, are either based on dimension reduction techniques, e.g., based on principal components, or directly based…

Statistics Theory · Mathematics 2026-01-23 Claudia Kirch , Hedvika Ranošová , Martin Wendler

This paper is mainly concerned with asymptotic studies of weighted bootstrap for u- and v-statistics. We derive the consistency of the weighted bootstrap u- and v-statistics, based on i.i.d. and non i.i.d. observations, from some more…

Statistics Theory · Mathematics 2012-10-23 Miklos Csorgo , Masoud M. Nasari

Kernel two-sample tests have been widely used, and the development of efficient methods for high-dimensional, large-scale data is receiving increasing attention in the big data era. However, existing methods, such as the maximum mean…

Methodology · Statistics 2025-10-03 Hoseung Song , Hao Chen

Although much progress has been made in the theory and application of bootstrap approximations for max statistics in high dimensions, the literature has largely been restricted to cases involving light-tailed data. To address this issue, we…

Methodology · Statistics 2025-12-24 Mingshuo Liu , Miles E. Lopes

It has been a long history in testing whether a mean vector with a fixed dimension has a specified value. Some well-known tests include the Hotelling $T^2$-test and the empirical likelihood ratio test proposed by Owen [Biometrika 75 (1988)…

Methodology · Statistics 2014-05-21 Liang Peng , Yongcheng Qi , Fang Wang

While an important topic in practice, the estimation of the number of non-noise components in blind source separation has received little attention in the literature. Recently, two bootstrap-based techniques for estimating the dimension…

Statistics Theory · Mathematics 2024-04-12 Joni Virta , Klaus Nordhausen

Recent results in quantization theory show that the mean-squared expected distortion can reach a rate of convergence of $\mathcal{O}(1/n)$, where $n$ is the sample size [see, e.g., IEEE Trans. Inform. Theory 60 (2014) 7279-7292 or Electron.…

Statistics Theory · Mathematics 2015-04-02 Clément Levrard

This paper studies the impact of bootstrap procedure on the eigenvalue distributions of the sample covariance matrix under a high-dimensional factor structure. We provide asymptotic distributions for the top eigenvalues of bootstrapped…

Statistics Theory · Mathematics 2023-11-21 Long Yu , Peng Zhao , Wang Zhou

We consider testing the significance of a subset of covariates in a nonparametric regression. These covariates can be continuous and/or discrete. We propose a new kernel-based test that smoothes only over the covariates appearing under the…

Statistics Theory · Mathematics 2014-03-28 Pascal Lavergne , Samuel Maistre , Valentin Patilea

We consider an analysis of variance type problem, where the sample observations are random elements in an infinite dimensional space. This scenario covers the case, where the observations are random functions. For such a problem, we propose…

Methodology · Statistics 2022-07-26 Joydeep Chowdhury , Probal Chaudhuri

The paper introduces a new kernel-based Maximum Mean Discrepancy (MMD) statistic for measuring the distance between two distributions given finitely-many multivariate samples. When the distributions are locally low-dimensional, the proposed…

Machine Learning · Statistics 2018-09-03 Xiuyuan Cheng , Alexander Cloninger , Ronald R. Coifman

One reason why standard formulations of the central limit theorems are not applicable in high-dimensional and non-stationary regimes is the lack of a suitable limit object. Instead, suitable distributional approximations can be used, where…

Statistics Theory · Mathematics 2024-12-20 Fabian Mies

Rotationally symmetric distributions on the p-dimensional unit hypersphere, extremely popular in directional statistics, involve a location parameter theta that indicates the direction of the symmetry axis. The most classical way of…

Statistics Theory · Mathematics 2014-02-13 Christophe Ley , Davy Paindaveine , Thomas Verdebout

This paper is to prove the asymptotic normality of a statistic for detecting the existence of heteroscedasticity for linear regression models without assuming randomness of covariates when the sample size $n$ tends to infinity and the…

Statistics Theory · Mathematics 2018-06-11 Zhidong Bai , Guangming Pan , Yanqing Yin

We propose a methodology for testing linear hypothesis in high-dimensional linear models. The proposed test does not impose any restriction on the size of the model, i.e. model sparsity or the loading vector representing the hypothesis.…

Methodology · Statistics 2019-07-09 Yinchu Zhu , Jelena Bradic

This paper explores hypothesis testing for the parametric forms of the mean and variance functions in regression models under diverging-dimension settings. To mitigate the curse of dimensionality, we introduce weighted residual empirical…

Statistics Theory · Mathematics 2025-10-28 Falong Tan , Xu Guo , Lixing Zhu

\cite{HillMotegi2017} present a new general asymptotic theory for the maximum of a random array $\{\mathcal{X}_{n}(i)$ $:$ $1$ $\leq $ $i$ $\leq $ $\mathcal{L}\}_{n\geq 1}$, where each $\mathcal{X}_{n}(i)$ is assumed to converge in…

Statistics Theory · Mathematics 2018-02-27 Jonathan B. Hill

The paper establishes the central limit theorems and proposes how to perform valid inference in factor models. We consider a setting where many counties/regions/assets are observed for many time periods, and when estimation of a global…

Econometrics · Economics 2023-06-22 Stanislav Anatolyev , Anna Mikusheva

Two-sample hypothesis testing-determining whether two sets of data are drawn from the same distribution-is a fundamental problem in statistics and machine learning with broad scientific applications. In the context of nonparametric testing,…

Machine Learning · Statistics 2026-04-21 Antoine Chatalic , Marco Letizia , Nicolas Schreuder , Lorenzo Rosasco