Related papers: High Dimensional Mean Test for Shrinking Random Va…
For a set of dependent random variables, without stationary or the strong mixing assumptions, we derive the asymptotic independence between their sums and maxima. Then we apply this result to high-dimensional testing problems, where we…
As an alternative to variable selection or shrinkage in high dimensional regression, we propose to randomly compress the predictors prior to analysis. This dramatically reduces storage and computational bottlenecks, performing well when the…
Robust statistics aims to compute quantities to represent data where a fraction of it may be arbitrarily corrupted. The most essential statistic is the mean, and in recent years, there has been a flurry of theoretical advancement for…
Tests based on sample mean vectors and sample spatial signs have been studied in the recent literature for high dimensional data with the dimension larger than the sample size. For suitable sequences of alternatives, we show that the powers…
We propose a two-sample mean test based on the Bayes factor with non-informative priors, specifically designed for scenarios where the dimension $p$ grows with the sample size $n$ with a linear rate $p/n \to c_1 \in (0, \infty)$. We…
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…
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…
This paper studies the problem of high-dimensional multiple testing and sparse recovery from the perspective of sequential analysis. In this setting, the probability of error is a function of the dimension of the problem. A simple…
A dimension reduction-based adaptive-to-model test is proposed for significance of a subset of covariates in the context of a nonparametric regression model. Unlike existing local smoothing significance tests, the new test behaves like a…
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 propose a new test of heteroscedasticity for parametric regression models and partial linear regression models in high dimensional settings. When the dimension of covariates is large, existing tests of heteroscedasticity…
This paper provides a framework for estimating the mean and variance of a high-dimensional normal density. The main setting considered is a fixed number of vector following a high-dimensional normal distribution with unknown mean and…
Principal component analysis continues to be a powerful tool in dimension reduction of high dimensional data. We assume a variance-diverging model and use the high-dimension, low-sample-size asymptotics to show that even though the…
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…
We introduce a very general method for sparse and large-scale variable selection. The large-scale regression settings is such that both the number of parameters and the number of samples are extremely large. The proposed method is based on…
This paper explores hypothesis testing for the parametric forms of the mean and variance functions in regression models under diverging-dimension settings. To mitigate the curse of dimensionality, we introduce weighted residual empirical…
In this paper, we investigate hypothesis testing for the linear combination of mean vectors across multiple populations through the method of random integration. We have established the asymptotic distributions of the test statistics under…
Residual marked empirical process-based tests are commonly used in regression models. However, they suffer from data sparseness in high-dimensional space when there are many covariates. This paper has three purposes. First, we suggest a…
Change point testing for high-dimensional data has attracted a lot of attention in statistics and machine learning owing to the emergence of high-dimensional data with structural breaks from many fields. In practice, when the dimension is…
High dimensional hypothesis test deals with models in which the number of parameters is significantly larger than the sample size. Existing literature develops a variety of individual tests. Some of them are sensitive to the dense and small…