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In this paper, we study three asymptotic regimes that can be applied to ranking and selection (R&S) problems with general sample distributions. These asymptotic regimes are constructed by sending particular problem parameters (probability…
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…
Several important families of computational and statistical results in machine learning and randomized algorithms rely on uniform bounds on quadratic forms of random vectors or matrices. Such results include the Johnson-Lindenstrauss (J-L)…
The classical likelihood ratio test (LRT) based on the asymptotic chi-squared distribution of the log likelihood is one of the fundamental tools of statistical inference. A recent universal LRT approach based on sample splitting provides…
We describe a new method for the random sampling of connected networks with a specified degree sequence. We consider both the case of simple graphs and that of loopless multigraphs. The constraints of fixed degrees and of connectedness are…
Since the two seminal papers by Fisher (1915, 1921) were published, the test under a fixed value correlation coefficient null hypothesis for the bivariate normal distribution constitutes an important statistical problem. In the framework of…
In modern data analysis, statistical efficiency improvement is expected via effective collaboration among multiple data holders with non-shared data. In this article, we propose a collaborative score-type test (CST) for testing linear…
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,…
We consider "randomized" statistics constructed by using a finite number of observations a random field at randomly chosen points. We generalize the invariance principle (the functional CLT), the Glivenko--Cantelli theorem, the theorem…
We consider sequences of symmetric $U$-statistics, not necessarily Hoeffding-degenerate, both in a one- and multi-dimensional setting, and prove quantitative central limit theorems (CLTs) based on the use of {\it contraction operators}. Our…
New tests are developed for two-way ANOVA models with heterogeneous error variances. The testing problems are considered for testing the significant interaction effects, simple effects, and treatment effects. The likelihood ratio tests…
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…
The main purpose of this paper is to present new families of test statistics for studying the problem of goodness-of-fit of some data to a latent class model for binary data. The families of test statistics introduced are based on…
We revisit the fundamental problem of learning with distribution shift, in which a learner is given labeled samples from training distribution $D$, unlabeled samples from test distribution $D'$ and is asked to output a classifier with low…
In bandit algorithms, the randomly time-varying adaptive experimental design makes it difficult to apply traditional limit theorems to off-policy evaluation of the treatment effect. Moreover, the normal approximation by the central limit…
The Dantzig selector (Candes and Tao, 2007) is a popular l1-regularization method for variable selection and estimation in linear regression. We present a very weak geometric condition on the observed predictors which is related to…
This paper presents a class of new algorithms for distributed statistical estimation that exploit divide-and-conquer approach. We show that one of the key benefits of the divide-and-conquer strategy is robustness, an important…
This paper proposes a class of origin-smooth approximators of indicators underlying the sum-of-negative-part statistic for testing multiple inequalities. The need for simulation or bootstrap to obtain test critical values is thereby…
We conduct a KL-divergence based procedure for testing elliptical distributions. The procedure simultaneously takes into account the two defining properties of an elliptically distributed random vector: independence between length and…
A randomized misfit approach is presented for the efficient solution of large-scale PDE-constrained inverse problems with high-dimensional data. The purpose of this paper is to offer a theory-based framework for random projections in this…