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Related papers: Deviation Tests for a High-dimensional Mean

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Heteroscedasticity testing is of importance in regression analysis. Existing local smoothing tests suffer severely from curse of dimensionality even when the number of covariates is moderate because of use of nonparametric estimation. In…

Methodology · Statistics 2015-10-14 Xuehu Zhu , Fei Chen , Xu Guo , Lixing Zhu

We propose two tests for the equality of covariance matrices between two high-dimensional populations. One test is on the whole variance--covariance matrices, and the other is on off-diagonal sub-matrices, which define the covariance…

Statistics Theory · Mathematics 2012-06-06 Jun Li , Song Xi Chen

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

We consider the problem of testing the mean of high-dimensional data when the dimension may grow without explicit rate restrictions relative to the sample size. The proposed procedure is based on the statistic V_n = n||Xn||^2, which avoids…

Statistics Theory · Mathematics 2026-05-18 Dietmar Ferger

This paper is concerned with testing global null hypotheses about population mean vectors of high-dimensional data. Current tests require either strong mixing (independence) conditions on the individual components of the high-dimensional…

Statistics Theory · Mathematics 2023-09-06 Alexander Giessing , Jianqing Fan

We characterize the fundamental limits of high-dimensional mean testing under arbitrary truncation, where samples are drawn from the conditional distribution $P(\cdot \mid S)$ for an unknown truncation set $S$ that may hide up to an…

Machine Learning · Statistics 2026-05-05 Yuhao Wang , Roberto Imbuzeiro Oliveira , Themis Gouleakis

This article deals with the problem of testing conditional independence between two random vectors ${\bf X}$ and ${\bf Y}$ given a confounding random vector ${\bf Z}$. Several authors have considered this problem for multivariate data.…

Statistics Theory · Mathematics 2025-09-16 Bilol Banerjee

We propose novel methodology for testing equality of model parameters between two high-dimensional populations. The technique is very general and applicable to a wide range of models. The method is based on sample splitting: the data is…

Methodology · Statistics 2013-01-17 Nicolas Städler , Sach Mukherjee

Two-sample inference for the difference of population means typically relies upon a Central Limit Theorem approximation. When data are drawn from a Negative Binomial distribution, previous work of Shilane et al. (2010) showed that a Normal…

Methodology · Statistics 2012-03-06 David Shilane , Derek Bean

This paper is focused on the moderate-deviations analysis of binary hypothesis testing. The analysis relies on a concentration inequality for discrete-parameter martingales with bounded jumps, where this inequality forms a refinement to the…

Information Theory · Computer Science 2016-11-17 Igal Sason

This paper considers the problem of estimating the variance of a sum of a triangular array of random vectors with heterogeneous means. When random vectors exhibit two-way cluster dependence or weak dependence, standard variance estimators…

Econometrics · Economics 2026-03-13 Luther Yap

The statistics and machine learning communities have recently seen a growing interest in classification-based approaches to two-sample testing. The outcome of a classification-based two-sample test remains a rejection decision, which is not…

Statistics Theory · Mathematics 2022-11-15 Loris Michel , Jeffrey Näf , Nicolai Meinshausen

We present differentially private algorithms for high-dimensional mean estimation. Previous private estimators on distributions over $\mathbb{R}^d$ suffer from a curse of dimensionality, as they require $\Omega(d^{1/2})$ samples to achieve…

Machine Learning · Computer Science 2024-11-04 Yuval Dagan , Michael I. Jordan , Xuelin Yang , Lydia Zakynthinou , Nikita Zhivotovskiy

Two parties observe independent copies of a $d$-dimensional vector and a scalar. They seek to test if their data is correlated or not, namely they seek to test if the norm $\|\rho\|_2$ of the correlation vector $\rho$ between their…

Information Theory · Computer Science 2020-05-22 K. R. Sahasranand , Himanshu Tyagi

Permutation tests are a distribution free way of performing hypothesis tests. These tests rely on the condition that the observed data are exchangeable among the groups being tested under the null hypothesis. This assumption is easily…

Methodology · Statistics 2017-12-14 Daniell Toth

In this paper new tests for the independence of two high-dimensional vectors are investigated. We consider the case where the dimension of the vectors increases with the sample size and propose multivariate analysis of variance-type…

Statistics Theory · Mathematics 2023-04-19 Taras Bodnar , Holger Dette , Nestor Parolya

This paper studies model checking for general parametric regression models having no dimension reduction structures on the predictor vector. Using any U-statistic type test as an initial test, this paper combines the sample-splitting and…

Methodology · Statistics 2023-08-21 Feng Liang , Chuhan Wang , jiaqi Huang , Lixing Zhu

The distribution function of a random distance in three dimensions is given and some new three-dimensional d2-tests of randomness are suggested. We show that our test statistics are not correlated with the usual test statistics and are…

Applications · Statistics 2014-02-24 Sergii Koliada

Maximum Mean Discrepancy (MMD) is a widely used concept in machine learning research which has gained popularity in recent years as a highly effective tool for comparing (finite-dimensional) distributions. Since it is designed as a…

Machine Learning · Statistics 2025-06-03 Andrew Alden , Blanka Horvath , Zacharia Issa

In this paper, we study a class of two sample test statistics based on inter-point distances in the high dimensional and low sample size setting. Our test statistics include the well-known energy distance and maximum mean discrepancy with…

Methodology · Statistics 2020-04-13 Changbo Zhu , Xiaofeng Shao