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A common problem in genetics is that of testing whether a set of highly dependent gene expressions differ between two populations, typically in a high-dimensional setting where the data dimension is larger than the sample size. Most…
For measuring the strength of visually-observed subpopulation differences, the Population Difference Criterion is proposed to assess the statistical significance of visually observed subpopulation differences. It addresses the following…
We propose a new testing procedure of heteroskedasticity in high-dimensional linear regression, where the number of covariates can be larger than the sample size. Our testing procedure is based on residuals of the Lasso. We demonstrate that…
In this paper, we study the detection boundary for minimax hypothesis testing in the context of high-dimensional, sparse binary regression models. Motivated by genetic sequencing association studies for rare variant effects, we investigate…
Nonparametric two sample testing deals with the question of consistently deciding if two distributions are different, given samples from both, without making any parametric assumptions about the form of the distributions. The current…
A central goal in experimental high energy physics is to detect new physics signals that are not explained by known physics. In this paper, we aim to search for new signals that appear as deviations from known Standard Model physics in…
Standardization has been a widely adopted practice in multiple testing, for it takes into account the variability in sampling and makes the test statistics comparable across different study units. However, despite conventional wisdom to the…
While there is considerable work on change point analysis in univariate time series, more and more data being collected comes from high dimensional multivariate settings. This paper introduces the asymptotic concept of high dimensional…
In this paper we study sharp thresholds for detecting sparse signals in $\beta$-models for potentially sparse random graphs. The results demonstrate interesting interplay between graph sparsity, signal sparsity, and signal strength. In…
We describe a novel non-parametric statistical hypothesis test of relative dependence between a source variable and two candidate target variables. Such a test enables us to determine whether one source variable is significantly more…
This paper considers testing linear hypotheses of a set of mean vectors with unequal covariance matrices in large dimensional setting. The problem of testing the hypothesis $H_0 : \sum_{i=1}^q \beta_i \bmu_i =\bmu_0 $ for a given vector…
In a case-control study aimed at localizing disease variants, association between a marker and the disease status is often tested by comparing the marker allele frequencies among cases and controls. These marker allele frequencies are…
The problem of detecting changes in covariance for a single pair of features has been studied in some detail, but may be limited in importance or general applicability. In contrast, testing equality of covariance matrices of a {\it set} of…
A Partial Conjunction Hypothesis (PCH) test combines information across a set of base hypotheses to determine whether some subset is non-null. PCH tests arise in a diverse array of fields, but standard PCH testing methods can be highly…
High-dimensional group inference is an essential part of statistical methods for analysing complex data sets, including hierarchical testing, tests of interaction, detection of heterogeneous treatment effects and inference for local…
Hierarchical inference in (generalized) regression problems is powerful for finding significant groups or even single covariates, especially in high-dimensional settings where identifiability of the entire regression parameter vector may be…
We introduce a rigorous and sensitive significance test for hyperuniformity that yields reliable results even from a single sample. Our approach is based on a detailed analysis of the empirical Fourier transform of a stationary point…
Due to their parsimony, separable covariance models have been popular in modeling matrix-variate data. However, the inference from such a model may be misleading if the population covariance matrix $\Sigma$ is actually non-separable,…
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…
Motivated by differential co-expression analysis in genomics, we consider in this paper estimation and testing of high-dimensional differential correlation matrices. An adaptive thresholding procedure is introduced and theoretical…