Related papers: Deviation Tests for a High-dimensional Mean
We introduce a new framework for the mean-variance spanning (MVS) hypothesis testing. The procedure can be applied to any test-asset dimension and only requires stationary asset returns and the number of benchmark assets to be smaller than…
While the problem of testing multivariate normality has received considerable attention in the classical low-dimensional setting where the sample size $n$ is much larger than the feature dimension $d$ of the data, there is presently a…
To date, testing interactions in high dimensions has been a challenging task. Existing methods often have issues with sensitivity to modeling assumptions and heavily asymptotic nominal p-values. To help alleviate these issues, we propose a…
Thanks to its favorable properties, the multivariate normal distribution is still largely employed for modeling phenomena in various scientific fields. However, when the number of components $p$ is of the same asymptotic order as the sample…
The two-sample problem, which consists in testing whether independent samples on $\mathbb{R}^d$ are drawn from the same (unknown) distribution, finds applications in many areas. Its study in high-dimension is the subject of much attention,…
In this article, we consider the problem of simultaneous testing of hypotheses when the individual test statistics are not necessarily independent. Specifically, we consider the problem of simultaneous testing of point null hypotheses…
A/B testing is widely used in modern technology companies for policy evaluation and product deployment, with the goal of comparing the outcomes under a newly-developed policy against a standard control. Various causal inference and…
The stochastic block model is a popular tool for detecting community structures in network data. Detecting the difference between two community structures is an important issue for stochastic block models. However, the two-sample test has…
The Maximum Mean Discrepancy (MMD) is a widely used multivariate distance metric for two-sample testing. The standard MMD test statistic has an intractable null distribution typically requiring costly resampling or permutation approaches…
The statistical analysis of discrete data has been the subject of extensive statistical research dating back to the work of Pearson. In this survey we review some recently developed methods for testing hypotheses about high-dimensional…
We study two-sample variable selection: identifying variables that discriminate between the distributions of two sets of data vectors. Such variables help scientists understand the mechanisms behind dataset discrepancies. Although…
Test of independence is of fundamental importance in modern data analysis, with broad applications in variable selection, graphical models, and causal inference. When the data is high dimensional and the potential dependence signal is…
Given a predictor of outcome derived from a high-dimensional dataset, pre-validation is a useful technique for comparing it to competing predictors on the same dataset. For microarray data, it allows one to compare a newly derived predictor…
We consider the problem of detecting a change in mean in a sequence of Gaussian vectors. Under the alternative hypothesis, the change occurs only in some subset of the components of the vector. We propose a test of the presence of a…
We study two-sample tests for relevant differences in persistence diagrams obtained from $L^p$-$m$-approximable data $(\mathcal{X}_t)_t$ and $(\mathcal{Y}_t)_t$. To this end, we compare variance estimates w.r.t.\ the Wasserstein metrics on…
Testing differences in mean vectors is a fundamental task in the analysis of high-dimensional compositional data. Existing methods may suffer from low power if the underlying signal pattern is in a situation that does not favor the deployed…
We test the null hypothesis that two parameters $(\mu_1,\mu_2)$ have the same sign, assuming that (asymptotically) normal estimators $(\hat{\mu}_1,\hat{\mu}_2)$ are available. Examples of this problem include the analysis of heterogeneous…
We propose a bootstrap-based test to detect a mean shift in a sequence of high-dimensional observations with unknown time-varying heteroscedasticity. The proposed test builds on the U-statistic based approach in Wang et al. (2022), targets…
Cumulative sum (CUSUM) statistics are widely used in the change point inference and identification. For the problem of testing for existence of a change point in an independent sample generated from the mean-shift model, we introduce a…
We consider the testing of mutual independence among all entries in a $d$-dimensional random vector based on $n$ independent observations. We study two families of distribution-free test statistics, which include Kendall's tau and…