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Distance correlation has become an increasingly popular tool for detecting the nonlinear dependence between a pair of potentially high-dimensional random vectors. Most existing works have explored its asymptotic distributions under the null…

Statistics Theory · Mathematics 2021-10-06 Lan Gao , Yingying Fan , Jinchi Lv , Qi-Man Shao

We propose a test of many zero parameter restrictions in a high dimensional linear iid regression model with $k$ $>>$ $n$ regressors. The test statistic is formed by estimating key parameters one at a time based on many low dimension…

Statistics Theory · Mathematics 2023-12-12 Jonathan B. Hill

Temporal data are increasingly prevalent in modern data science. A fundamental question is whether two time series are related or not. Existing approaches often have limitations, such as relying on parametric assumptions, detecting only…

Machine Learning · Statistics 2024-05-29 Cencheng Shen , Jaewon Chung , Ronak Mehta , Ting Xu , Joshua T. Vogelstein

In this paper, we study change-point testing for high-dimensional linear models, an important problem that has not been well explored in the literature. Specifically, we propose a quadratic-form cumulative sum (CUSUM) statistic to test the…

Statistics Theory · Mathematics 2024-10-23 Zifeng Zhao , Xiaokai Luo , Zongge Liu , Daren Wang

In this paper, we consider procedures for testing hypotheses on the dimension of the linear span generated by a growing number of $p\times p$ covariance matrices from independent $q$ populations. Under a proper limiting scheme where all the…

Statistics Theory · Mathematics 2026-02-16 Tianxing Mei , Chen Wang , Jianfeng Yao

In this paper, we address the problem of testing independence between two high-dimensional random vectors. Our approach involves a series of max-sum tests based on three well-known classes of rank-based correlations. These correlation…

Methodology · Statistics 2024-04-04 Hongfei Wang , Binghui Liu , Long Feng

High-dimensional vector autoregression with measurement error is frequently encountered in a large variety of scientific and business applications. In this article, we study statistical inference of the transition matrix under this model.…

Methodology · Statistics 2020-09-18 Xiang Lyu , Jian Kang , Lexin Li

In the statistical inference for long range dependent time series the shape of the limit distribution typically depends on unknown parameters. Therefore, we propose to use subsampling. We show the validity of subsampling for general…

Statistics Theory · Mathematics 2016-10-20 Annika Betken , Martin Wendler

We consider the estimation of large covariance and precision matrices from high-dimensional sub-Gaussian or heavier-tailed observations with slowly decaying temporal dependence. The temporal dependence is allowed to be long-range so with…

Statistics Theory · Mathematics 2019-12-23 Hai Shu , Bin Nan

We derive a scale-free bound on the density of the maximum of a centered Gaussian vector. The basic bound is non-uniform, depends logarithmically on the dimension, and allows any covariance matrix. When the largest marginal variance is…

Statistics Theory · Mathematics 2026-05-29 Suhas Vijaykumar

This paper shows that the problem of testing hypotheses in moment condition models without any assumptions about identification may be considered as a problem of testing with an infinite-dimensional nuisance parameter. We introduce a…

Statistics Theory · Mathematics 2014-09-24 Isaiah Andrews , Anna Mikusheva

We take a different look at the problem of testing the independence of two metric-space-valued random variables using the distance correlation. Instead of testing if the distance correlation vanishes exactly, we are interested in the…

Statistics Theory · Mathematics 2025-11-19 Holger Dette , Marius Kroll

Given observations from a stationary time series, permutation tests allow one to construct exactly level $\alpha$ tests under the null hypothesis of an i.i.d. (or, more generally, exchangeable) distribution. On the other hand, when the null…

Statistics Theory · Mathematics 2020-09-09 Joseph P. Romano , Marius A. Tirlea

We develop a class of optimal tests for a structural break occurring at an unknown date in infinite and growing-order time series regression models, such as AR($\infty$), linear regression with increasingly many covariates, and…

Econometrics · Economics 2025-10-15 Abhimanyu Gupta , Myung Hwan Seo

Variance estimation is important for statistical inference. It becomes non-trivial when observations are masked by serial dependence structures and time-varying mean structures. Existing methods either ignore or sub-optimally handle these…

Methodology · Statistics 2022-01-03 Kin Wai Chan

We develop a testing procedure for distinguishing between a long-range dependent time series and a weakly dependent time series with change-points in the mean. In the simplest case, under the null hypothesis the time series is weakly…

Statistics Theory · Mathematics 2016-08-16 István Berkes , Lajos Horváth , Piotr Kokoszka , Qi-Man Shao

Multivariate locally stationary functional time series provide a flexible framework for modeling complex data structures exhibiting both temporal and spatial dependencies while allowing for time-varying data generating mechanism. In this…

Methodology · Statistics 2025-01-15 Lujia Bai , Holger Dette , Weichi Wu

In this paper, we consider the problem of testing equality of the covariance matrices of L complex Gaussian multivariate time series of dimension $M$ . We study the special case where each of the L covariance matrices is modeled as a rank K…

Statistics Theory · Mathematics 2024-04-11 Rémi Beisson , Pascal Vallet , Audrey Giremus , Guillaume Ginolhac

This paper investigates the utilization of maximum and average distance correlations for multivariate independence testing. We characterize their consistency properties in high-dimensional settings with respect to the number of marginally…

Machine Learning · Statistics 2025-06-11 Cencheng Shen , Yuexiao Dong

We propose a novel method for testing serial independence of object-valued time series in metric spaces, which is more general than Euclidean or Hilbert spaces. The proposed method is fully nonparametric, free of tuning parameters, and can…

Methodology · Statistics 2023-07-31 Feiyu Jiang , Hanjia Gao , Xiaofeng Shao