Related papers: Spatial-Sign based High-Dimensional Location Test

We summarize properties of the spatial sign covariance matrix and especially look at the relationship between its eigenvalues and those of the shape matrix of an elliptical distribution. The explicit relationship known in the bivariate case…

We consider the hypothesis testing problem of detecting a shift between the means of two multivariate normal distributions in the high-dimensional setting, allowing for the data dimension p to exceed the sample size n. Specifically, we…

We consider inference on the first principal direction of a $p$-variate elliptical distribution. We do so in challenging double asymptotic scenarios for which this direction eventually fails to be identifiable. In order to achieve…

Due to the broad applications of elliptical models, there is a long line of research on goodness-of-fit tests for empirically validating them. However, the existing literature on this topic is generally confined to low-dimensional settings,…

The sign test (Arbuthnott, 1710) and the Wilcoxon signed-rank test (Wilcoxon, 1945) are among the first examples of a nonparametric test. These procedures -- based on signs, (absolute) ranks and signed-ranks -- yield distribution-free tests…

In this article, we propose a class of test statistics for a change point in the mean of high-dimensional independent data. Our test integrates the U-statistic based approach in a recent work by \cite{hdcp} and the $L_q$-norm based…

In this paper, we propose a power comparison between high dimensional t-test, sign and signed rank test for the one sample mean test. We show that the high dimensional signed rank test is superior to a high dimensional t test, but inferior…

We present a computational strategy for reducing the sign problem in the evaluation of high dimensional integrals with non-positive definite weights. The method involves stochastic sampling with a positive semidefinite weight that is…

Testing for the equality of two high-dimensional distributions is a challenging problem, and this becomes even more challenging when the sample size is small. Over the last few decades, several graph-based two-sample tests have been…

We propose a flexible and robust nonparametric framework for testing spatial dependence in two- and three-dimensional random fields. Our approach involves converting spatial data into one-dimensional time series using space-filling Hilbert…

In this paper, for the problem of heteroskedastic general linear hypothesis testing (GLHT) in high-dimensional settings, we propose a random integration method based on the reference L2-norm to deal with such problems. The asymptotic…

We are concerned with the detection of associations between random vectors of any dimension. Few tests of independence exist that are consistent against all dependent alternatives. We propose a powerful test that is applicable in all…

We consider the problem of testing the stationarity and isotropy of a spatial point pattern based on the concept of local spectra. Using a logarithmic transformation, the mechanism of the proposed test is approximately identical to a simple…

Size distortion can occur if an asymptotic testing procedure requiring diverging sample sizes, is implemented to data with very small sample sizes. In this paper, we consider one-sample and two-sample tests for mean vectors when data are…

We address high dimensional covariance estimation for elliptical distributed samples, which are also known as spherically invariant random vectors (SIRV) or compound-Gaussian processes. Specifically we consider shrinkage methods that are…

Multivariate sign functions are often used for robust estimation and inference. We propose using data dependent weights in association with such functions. The proposed weighted sign functions retain desirable robustness properties, while…

High-dimensional data arise routinely in modern statistics, econometrics, finance, genomics, and machine learning. While a large body of existing methodology is developed under Gaussian or light-tailed assumptions, many real data sets…

In this paper, we study a class of two sample test statistics based on inter-point distances in the high dimensional and low sample size setting. Our test statistics include the well-known energy distance and maximum mean discrepancy with…

We develop goodness-of-fit tests for max-stable random fields, which are used to model heavy-tailed spatial data. The test statistics are constructed based on the Fourier transforms of the indicators of extreme values in the heavy-tailed…

We consider linear models with scalar responses and covariates from a separable Hilbert space. The aim is to detect change points in the error distribution, based on sequential residual empirical distribution functions. Expansions for those…