Related papers: A More Powerful Two-Sample Test in High Dimensions…
We present the results of a large number of simulation studies regarding the power of various non-parametric two-sample tests for multivariate data. This includes both continuous and discrete data. In general no single method can be relied…
Nonparametric generalized likelihood ratio test is popularly used for model checking for regressions. However, there are two issues that may be the barriers for its powerfulness. First, the bias term in its liming null distribution causes…
This article develops a framework for testing general hypothesis in high-dimensional models where the number of variables may far exceed the number of observations. Existing literature has considered less than a handful of hypotheses, such…
In the problem of composite hypothesis testing, identifying the potential uniformly most powerful (UMP) unbiased test is of great interest. Beyond typical hypothesis settings with exponential family, it is usually challenging to prove the…
We present a simple method for assessing the predictive performance of high-dimensional models directly in data space when only samples are available. Our approach is to compare the quantiles of observables predicted by a model to those of…
This paper is motivated by the analysis of gene expression sets, especially by finding differentially expressed gene sets between two phenotypes. Gene $\log_2$ expression levels are highly correlated and, very likely, have approximately…
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…
Data with multiple functional recordings at each observational unit are increasingly common in various fields including medical imaging and environmental sciences. To conduct inference for such observations, we develop a paired two-sample…
In this work, we introduce statistical testing under distributional shifts. We are interested in the hypothesis $P^* \in H_0$ for a target distribution $P^*$, but observe data from a different distribution $Q^*$. We assume that $P^*$ is…
It is quite common in modern research, for a researcher to test many hypotheses. The statistical (frequentist) hypothesis testing framework, does not scale with the number of hypotheses in the sense that naively performing many hypothesis…
We consider two alternative tests to the Higher Criticism test of Donoho and Jin [Ann. Statist. 32 (2004) 962-994] for high-dimensional means under the sparsity of the nonzero means for sub-Gaussian distributed data with unknown column-wise…
We consider linear regression in the high-dimensional regime where the number of observations $n$ is smaller than the number of parameters $p$. A very successful approach in this setting uses $\ell_1$-penalized least squares (a.k.a. the…
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…
This paper develops a novel methodology for testing the goodness-of-fit of sparse parametric regression models based on projected empirical processes and p-value combination, where the covariate dimension may substantially exceed the sample…
We investigate one/two-sample mean tests for high-dimensional compositional data when the number of variables is comparable with the sample size, as commonly encountered in microbiome research. Existing methods mainly focus on max-type test…
We present a study of a kernel-based two-sample test statistic related to the Maximum Mean Discrepancy (MMD) in the manifold data setting, assuming that high-dimensional observations are close to a low-dimensional manifold. We characterize…
External controls from historical trials or observational data can augment randomized controlled trials when large-scale randomization is impractical or unethical, such as in drug evaluation for rare diseases. However, non-randomized…
Two-sample hypothesis testing for random graphs arises naturally in neuroscience, social networks, and machine learning. In this paper, we consider a semiparametric problem of two-sample hypothesis testing for a class of latent position…
The power of multiple testing procedures can be increased by using weighted p-values (Genovese, Roeder and Wasserman 2005). We derive the optimal weights and we show that the power is remarkably robust to misspecification of these weights.…
High-dimensional data sets are commonly collected in many contemporary applications arising in various fields of scientific research. We present two views of finite samples in high dimensions: a probabilistic one and a nonprobabilistic one.…