Estimation of multiple mean vectors in high dimension

arXiv:2403.15038v1 Announce Type: cross
Abstract: We endeavour to estimate numerous multi-dimensional means of various probability distributions on a common space based on independent samples. Our approach involves forming estimators through convex combinations of empirical means derived from these samples. We introduce two strategies to find appropriate data-dependent convex combination weights: a first one employing a testing procedure to identify neighbouring means with low variance, which results in a closed-form plug-in formula for the weights, and a second one determining weights …

abstract arxiv combination cs.lg data independent mean multiple probability samples space stat.ml strategies through type vectors