Robust High-dimensional Tuning Free Multiple Testing. (arXiv:2211.11959v2 [math.ST] UPDATED)

A stylized feature of high-dimensional data is that many variables have heavy
tails, and robust statistical inference is critical for valid large-scale
statistical inference. Yet, the existing developments such as Winsorization,
Huberization and median of means require the bounded second moments and involve
variable-dependent tuning parameters, which hamper their fidelity in
applications to large-scale problems. To liberate these constraints, this paper
revisits the celebrated Hodges-Lehmann (HL) estimator for estimating location
parameters in both the one- and two-sample problems, from a …

arxiv free math multiple testing