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Related papers: On testing for high-dimensional white noise

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Analyzing large samples of high-dimensional data under dependence is a challenging statistical problem as long time series may have change points, most importantly in the mean and the marginal covariances, for which one needs valid tests.…

Methodology · Statistics 2022-11-07 Fabian Mies , Ansgar Steland

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 dependence and the resulting autocovariances in time series data can introduce bias into ANOVA test statistics, thereby affecting their size and power. This manuscript accounts for temporal dependence in ANOVA and develops a test…

Statistics Theory · Mathematics 2025-09-12 Yunyi Zhang

Drawing statistical inferences from large datasets in a model-robust way is an important problem in statistics and data science. In this paper, we propose methods that are robust to large and unequal noise in different observational units…

Statistics Theory · Mathematics 2024-01-10 Edgar Dobriban , Weijie J. Su , Yachong Yang , Zhixiang Zhang

We consider a $d$-dimensional continuous martingale $X(t)$ with quadratic variation matrix $\langle X\rangle_t=\int_0^t \Sigma(s)\,ds$ and develop tests for the rank of its spot covariance matrix $\Sigma(t)$, $t\in[0,1]$. The process $X$ is…

Statistics Theory · Mathematics 2026-01-14 Markus Reiß , Lars Winkelmann

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

The problem of testing changes in covariance has received increasing attention in recent years, especially in the context of high-dimensional testing. A number of approaches have been proposed, all limited to the two-sample problem and…

Methodology · Statistics 2016-09-06 Yi-Hui Zhou

We consider the problem of detecting deviations from a white noise assumption in time series. Our approach differs from the numerous methods proposed for this purpose with respect to two aspects. First, we allow for non-stationary time…

Statistics Theory · Mathematics 2024-11-12 Patrick Bastian

We propose a likelihood ratio test framework for testing normal mean vectors in high-dimensional data under two common scenarios: the one-sample test and the two-sample test with equal covariance matrices. We derive the test statistics…

Methodology · Statistics 2018-09-25 Zongliang Hu , Tiejun Tong , Marc G. Genton

In this paper, we consider tests for ultrahigh-dimensional partially linear regression models. The presence of ultrahigh-dimensional nuisance covariates and unknown nuisance function makes the inference problem very challenging. We adopt…

Methodology · Statistics 2023-04-18 Hongwei Shi , Bowen Sun , Weichao Yang , Xu Guo

Independent or i.i.d. innovations is an essential assumption in the literature for analyzing a vector time series. However, this assumption is either too restrictive for a real-life time series to satisfy or is hard to verify through a…

Statistics Theory · Mathematics 2023-10-12 Yunyi Zhang

We propose a new testing procedure of heteroskedasticity in high-dimensional linear regression, where the number of covariates can be larger than the sample size. Our testing procedure is based on residuals of the Lasso. We demonstrate that…

Statistics Theory · Mathematics 2022-11-01 Akira Shinkyu

Traditional white noise testing, for example the Ljung-Box test, studies only the autocorrelation function (ACF). Time series can be heteroscedastic and therefore not i.i.d. but still white noise (that is, with zero ACF). An example of…

Statistics Theory · Mathematics 2022-03-25 Andrey Sarantsev

In this paper, we propose a novel approach to test the equality of high-dimensional mean vectors of several populations via the weighted $L_2$-norm. We establish the asymptotic normality of the test statistics under the null hypothesis. We…

Statistics Theory · Mathematics 2024-02-01 Jianghao Li , Zhenzhen Niu , Shizhe Hong , Zhidong Bai

We investigate the problem of testing the global null in the high-dimensional regression models when the feature dimension $p$ grows proportionally to the number of observations $n$. Despite a number of prior work studying this problem,…

Methodology · Statistics 2020-10-06 Yue Li , Ilmun Kim , Yuting Wei

In this article, we propose a class of $L_q$-norm based U-statistics for a family of global testing problems related to high-dimensional data. This includes testing of mean vector and its spatial sign, simultaneous testing of linear model…

Statistics Theory · Mathematics 2023-03-16 Yangfan Zhang , Runmin Wang , Xiaofeng Shao

We propose a high dimensional mean test framework for shrinking random variables, where the underlying random variables shrink to zero as the sample size increases. By pooling observations across overlapping subsets of dimensions, we…

Methodology · Statistics 2026-02-11 Liujun Chen , Chen Zhou

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

We develop a unified $L$-statistic testing framework for high-dimensional regression coefficients that adapts to unknown sparsity. The proposed statistics rank coordinate-wise evidence measures and aggregate the top $k$ signals, bridging…

Applications · Statistics 2026-02-10 Ping Zhao , Fengyi Song , Huifang Ma

We propose a general white noise test for functional time series based on estimating a distance between the spectral density operator of a weakly stationary time series and the constant spectral density operator of an uncorrelated time…

Statistics Theory · Mathematics 2020-07-07 Vaidotas Characiejus , Gregory Rice