5 papers · 1 filter
Adversarially robust multiple testing in high dimensions
Anders Bredahl Kock, David Preinerstorfer
Robust multiple testing procedures for assessing equality restrictions on the coordinates of high-dimensional mean vectors are proposed. Our procedures are based on quantile-winsor…
Robustness for free: asymptotic size and power of max-tests in high dimensions
Anders Bredahl Kock, David Preinerstorfer
Allowing for adversarial contamination and heavy tails, we study testing whether the mean of a high-dimensional random vector equals zero. Because standard max-tests based on sampl…
Winsorized mean estimation with heavy tails and adversarial contamination
Anders Bredahl Kock, David Preinerstorfer
Finite-sample upper bounds on the estimation error of a winsorized mean estimator of the population mean in the presence of heavy tails and adversarial contamination are establishe…
High-dimensional Gaussian and bootstrap approximations for robust means
Anders Bredahl Kock, David Preinerstorfer
Recent years have witnessed much progress on Gaussian and bootstrap approximations to the distribution of sums of independent random vectors with dimension large relative to th…
A remark on moment-dependent phase transitions in high-dimensional Gaussian approximations
Anders Bredahl Kock, David Preinerstorfer
In this article, we study the critical growth rates of dimension below which Gaussian critical values can be used for hypothesis testing but beyond which they cannot. We are partic…