Related papers: Two-sample tests for high-dimension, strongly spik…
We consider classifiers for high-dimensional data under the strongly spiked eigenvalue (SSE) model. We first show that high-dimensional data often have the SSE model. We consider a distance-based classifier using eigenstructures for the SSE…
In this paper, we study the asymptotic behavior of the extreme eigenvalues and eigenvectors of the high dimensional spiked sample covariance matrices, in the supercritical case when a reliable detection of spikes is possible. Especially, we…
To understand how neural networks process information, it is important to investigate how neural network dynamics varies with respect to different stimuli. One challenging task is to design efficient statistical approaches to analyze…
We propose a two-sample testing procedure based on learned deep neural network representations. To this end, we define two test statistics that perform an asymptotic location test on data samples mapped onto a hidden layer. The tests are…
We consider general high-dimensional spiked sample covariance models and show that their leading sample spiked eigenvalues and their linear spectral statistics are asymptotically independent when the sample size and dimension are…
Sample covariance matrices from multi-population typically exhibit several large spiked eigenvalues, which stem from differences between population means and are crucial for inference on the underlying data structure. This paper…
This paper aims to test the number of spikes in a generalized spiked covariance matrix, the spiked eigenvalues of which may be extremely larger or smaller than the non-spiked ones. For a high-dimensional problem, we first propose a general…
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…
This paper investigates a statistical procedure for testing the equality of two independent estimated covariance matrices when the number of potentially dependent data vectors is large and proportional to the size of the vectors, that is,…
In a spiked population model, the population covariance matrix has all its eigenvalues equal to units except for a few fixed eigenvalues (spikes). Determining the number of spikes is a fundamental problem which appears in many scientific…
Robust classification algorithms have been developed in recent years with great success. We take advantage of this development and recast the classical two-sample test problem in the framework of classification. Based on the estimates of…
We consider the five classes of multivariate statistical problems identified by James (1964), which together cover much of classical multivariate analysis, plus a simpler limiting case, symmetric matrix denoising. Each of James' problems…
This paper investigates a statistical procedure for testing the equality of two independently estimated covariance matrices when the number of potentially dependent data vectors is large and proportional to the size of the vectors, that is,…
Data depth has been applied as a nonparametric measurement for ranking multivariate samples. In this paper, we focus on homogeneity tests to assess whether two multivariate samples are from the same distribution. There are many data…
We introduce a new method for two-sample testing of high-dimensional linear regression coefficients without assuming that those coefficients are individually estimable. The procedure works by first projecting the matrices of covariates and…
This paper investigates a statistical procedure for testing the equality of two independent estimated covariance matrices when the number of potentially dependent data vectors is large and proportional to the size of the vectors, that is,…
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…
In this article, we propose some two-sample tests based on ball divergence and investigate their high dimensional behavior. First, we study their behavior for High Dimension, Low Sample Size (HDLSS) data, and under appropriate regularity…
In this paper, we introduce an innovative testing procedure for assessing individual hypotheses in high-dimensional linear regression models with measurement errors. This method remains robust even when either the X-model or Y-model is…
A two-sample hypothesis test is a statistical procedure used to determine whether the distributions generating two samples are identical. We consider the two-sample testing problem in a new scenario where the sample measurements (or sample…