Time-Uniform Confidence Spheres for Means of Random Vectors

arXiv:2311.08168v2 Announce Type: replace-cross
Abstract: We derive and study time-uniform confidence spheres -- confidence sphere sequences (CSSs) -- which contain the mean of random vectors with high probability simultaneously across all sample sizes. Inspired by the original work of Catoni and Giulini, we unify and extend their analysis to cover both the sequential setting and to handle a variety of distributional assumptions. Our results include an empirical-Bernstein CSS for bounded random vectors (resulting in a novel empirical-Bernstein confidence interval with …

abstract analysis arxiv confidence cs.it math.it math.st mean probability random sample sphere stat.me stat.ml stat.th study type uniform vectors work