Related papers: Note on Mean Vector Testing for High-Dimensional D…
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…
This paper deals with the asymptotic statistical properties of a class of redescending M-estimators in linear models with increasing dimension. This class is wide enough to include popular high breakdown point estimators such as…
We develop an asymptotic theory for $L^2$ norms of sample mean vectors of high-dimensional data. An invariance principle for the $L^2$ norms is derived under conditions that involve a delicate interplay between the dimension $p$, the sample…
For testing the independence of two vectors with respective dimensions $p_1$ and $p_2$, the existing literature in high-dimensional statistics all assume that both dimensions $p_1$ and $p_2$ grow to infinity with the sample size. However,…
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…
This paper considers the problem of testing temporal homogeneity of $p$-dimensional population mean vectors from the repeated measurements of $n$ subjects over $T$ times. To cope with the challenges brought by high-dimensional longitudinal…
We consider the change point testing problem for high-dimensional time series. Unlike conventional approaches, where one tests whether the difference $\delta$ of the mean vectors before and after the change point is equal to zero, we argue…
Many high-dimensional hypothesis tests aim to globally examine marginal or low-dimensional features of a high-dimensional joint distribution, such as testing of mean vectors, covariance matrices and regression coefficients. This paper…
In this paper, we study the problem of testing the mean vectors of high dimensional data in both one-sample and two-sample cases. The proposed testing procedures employ maximum-type statistics and the parametric bootstrap techniques to…
Hotelling's T-squared test is a classical tool to test if the normal mean of a multivariate normal distribution is a specified one or the means of two multivariate normal means are equal. When the population dimension is higher than the…
We consider the problem of detecting distributional changes in a sequence of high dimensional data. Our approach combines two separate statistics stemming from $L_p$ norms whose behavior is similar under $H_0$ but potentially different…
This paper investigates testing for deviation of a high-dimensional mean vector $\boldsymbol{\mu}$. In contrast to the standard one-sample significance test of the form: $H_0^\texttt{e} : \boldsymbol{\mu} = \boldsymbol{\mu}_0$ versus…
While there is considerable work on change point analysis in univariate time series, more and more data being collected comes from high dimensional multivariate settings. This paper introduces the asymptotic concept of high dimensional…
Many statistical methodologies for high-dimensional data assume the population is normal. Although a few multivariate normality tests have been proposed, to the best of our knowledge, none of them can properly control the type I error when…
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…
In this paper, we propose a class of monitoring statistics for a mean shift in a sequence of high-dimensional observations. Inspired by the recent U-statistic based retrospective tests developed by Wang et al.(2019) and Zhang et al.(2020),…
High-dimensional data, where the dimension of the feature space is much larger than sample size, arise in a number of statistical applications. In this context, we construct the generalized multivariate sign transformation, defined as a…
High-dimensional time series are characterized by a large number of measurements and complex dependence, and often involve abrupt change points. We propose a new procedure to detect change points in the mean of high-dimensional time series…
Recently, Tibshirani et al. (2016) proposed a method for making inferences about parameters defined by model selection, in a typical regression setting with normally distributed errors. Here, we study the large sample properties of this…
This paper proposes a new mutual independence test for a large number of high dimensional random vectors. The test statistic is based on the characteristic function of the empirical spectral distribution of the sample covariance matrix. The…