Robust multiple testing procedures for assessing equality restrictions on the coordinates of high-dimensional mean vectors are proposed. Our procedures are based on quantile-winsorization techniques, approximately control the familywise error rate (strongly) under adversarial contamination, and allow the number of hypotheses to grow exponentially with sample size, despite requiring only slightly more than two moments. Technically, our one-sample results build on recent Gaussian approximation inequalities for the distribution of high-dimensional quantile-winsorized means, whereas our two-sample results are based on extensions thereof, which we develop here and which could be of some interest in their own right.
Because 2SLS is built from sample averages, a small number of observations can have a disproportionate effect on estimates and inference. We introduce W-2SLS, a simple drop-in robustification that replaces these averages by quantile-winsorized means. We analyze W-2SLS under adversarial contamination, which permits both...
This work proposes the first robust estimator achieving near-optimal dimension-free statistical rates in this setting, and extends the trimmed-mean framework underlying recent advances in robust mean and covariance estimation to arbitrary tensor order.
R. Oliveira, Zoraida F. Rico, Philip Thompson· 0 citations
This work proposes computationally efficient tests for equality of mean vectors of two or more high-dimensional populations by establishing an equivalence between equality of means and a zero population logistic regression parameter.
It is proved that VC classes are adversarially robustly learnable with sample complexity linear in the VC dimension $d$, providing an exponential improvement over the previous upper bound of Montasser, Hanneke, and Srebro (2019).
The purpose of this paper is to rigorously quantify the statistical and learning-theoretic properties of adversarial training models for classification. Equivalently, we establish the statistical properties of empirical optimal partial transport. Precisely, first we provide two types of central limit theorems (CLT): CL...
This work studies norm-constrained linear classification under Euclidean adversarial perturbations in a Gaussian model with a low-dimensional informative subspace and an independent noise tail to establish a unique population minimizer and joint local growth.
