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Related papers: On testing for high-dimensional white noise

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This paper investigates the signal detection problem in colored noise with an unknown covariance matrix. In particular, we focus on detecting an unknown non-random signal by capitalizing on the leading eigenvalue of the whitened sample…

Signal Processing · Electrical Eng. & Systems 2024-02-01 Prathapasinghe Dharmawansa , Saman Atapattu , Jamie Evans , Kandeepan Sithamparanathan

This paper develops a novel methodology for testing the goodness-of-fit of sparse parametric regression models based on projected empirical processes and p-value combination, where the covariate dimension may substantially exceed the sample…

Statistics Theory · Mathematics 2026-01-05 Falong Tan , Shan Tang , Lixing Zhu

Principal component analysis (PCA) is a well-known tool in multivariate statistics. One significant challenge in using PCA is the choice of the number of components. In order to address this challenge, we propose an exact distribution-based…

Methodology · Statistics 2015-06-02 Yunjin Choi , Jonathan Taylor , Robert Tibshirani

We obtain general, exact formulas for the overlaps between the eigenvectors of large correlated random matrices, with additive or multiplicative noise. These results have potential applications in many different contexts, from quantum…

Statistical Mechanics · Physics 2018-12-05 Joël Bun , Jean-Philippe Bouchaud , Marc Potters

In this paper we initiate the study of whether or not sparse estimation tasks can be performed efficiently in high dimensions, in the robust setting where an $\eps$-fraction of samples are corrupted adversarially. We study the natural…

Machine Learning · Computer Science 2017-03-02 Jerry Li

For high-dimensional small sample size data, Hotelling's T2 test is not applicable for testing mean vectors due to the singularity problem in the sample covariance matrix. To overcome the problem, there are three main approaches in the…

Methodology · Statistics 2020-03-11 Zongliang Hu , Tiejun Tong , Marc G. Genton

A spatial-sign based test procedure is proposed for high dimensional white noise test in this paper. We establish the limit null distribution and give the asymptotical relative efficient of our test with respect to the test proposed by Feng…

Statistics Theory · Mathematics 2023-03-21 Ping Zhao , Dachuan Chen , Zhaojun Wang

Fitting high-dimensional statistical models often requires the use of non-linear parameter estimation procedures. As a consequence, it is generally impossible to obtain an exact characterization of the probability distribution of the…

Methodology · Statistics 2014-04-03 Adel Javanmard , Andrea Montanari

In this article, we focus on the problem of testing the equality of several high dimensional mean vectors with unequal covariance matrices. This is one of the most important problem in multivariate statistical analysis and there have been…

Statistics Theory · Mathematics 2015-04-28 Jiang Hu , Zhidong Bai , Chen Wang , Wei Wang

Principal component analysis (PCA) is a widely used method for dimension reduction. In high dimensional data, the "signal" eigenvalues corresponding to weak principal components (PCs) do not necessarily separate from the bulk of the "noise"…

Statistics Theory · Mathematics 2017-10-03 Edgar Dobriban

In this paper, we consider a system of $k$ second order non-linear stochastic partial differential equations with spatial dimension $d \geq 1$, driven by a $q$-dimensional Gaussian noise, which is white in time and with some spatially…

Probability · Mathematics 2011-02-17 Eulalia Nualart

We consider inference problems for high-dimensional (HD) functional data with a dense number (T) of repeated measurements taken for a large number of p variables from a small number of n experimental units. The spatial and temporal…

Methodology · Statistics 2020-05-06 Shawn Santo , Ping-Shou Zhong

Detection of the number of signals corrupted by high-dimensional noise is a fundamental problem in signal processing and statistics. This paper focuses on a general setting where the high-dimensional noise has an unknown complicated…

Statistics Theory · Mathematics 2022-05-16 Xiucai Ding , Fan Yang

In this article, we first establish the joint central limit theorem (CLT) for the extreme eigenvalues of the sample correlation matrix of high-dimensional random walks with cross-sectional dependence. We further investigate the asymptotic…

Methodology · Statistics 2025-08-05 Ruihan Liu , Chen Wang

Modern data are increasingly both high-dimensional and heteroscedastic. This paper considers the challenge of estimating underlying principal components from high-dimensional data with noise that is heteroscedastic across samples, i.e.,…

Statistics Theory · Mathematics 2022-09-14 David Hong , Fan Yang , Jeffrey A. Fessler , Laura Balzano

Consider the empirical autocovariance matrix at a given non-zero time lag based on observations from a multivariate complex Gaussian stationary time series. The spectral analysis of these autocovariance matrices can be useful in certain…

Statistics Theory · Mathematics 2022-06-01 Arup Bose , Walid Hachem

In this paper, we develop invariance-based procedures for testing and inference in high-dimensional regression models. These procedures, also known as randomization tests, provide several important advantages. First, for the global null…

Methodology · Statistics 2023-12-27 Wenxuan Guo , Panos Toulis

We consider testing zero pricing errors in high-dimensional linear factor pricing models. Existing methods are mainly based on either an $L_2$ statistic, which is effective under dense alternatives, or an $L_\infty$ statistic, which is…

Methodology · Statistics 2026-04-01 Ping Zhao , Huifang Ma , Long Feng

In this paper a robust version of the classical Wald test statistics for linear hypothesis in the logistic regression model is introduced and its properties are explored. We study the problem under the assumption of random covariates…

Statistics Theory · Mathematics 2019-05-09 Ayandrendanath Basu , Abhik Ghosh , Abhijit Mandal , Nirian Martin , Leandro Pardo

This paper deals with the local asymptotic structure, in the sense of Le Cam's asymptotic theory of statistical experiments, of the signal detection problem in high dimension. More precisely, we consider the problem of testing the null…

Statistics Theory · Mathematics 2012-10-23 Alexei Onatski , Marcelo J. Moreira , Marc Hallin