Confidence Sets for a Multivariate Distribution

Abstract

The confidence sets for a q-dimensional distribution studied in this paper have several attractive features: affine invariance, correct asymptotic level whatever the actual distribution may be, numerical feasibility, and a local asymptotic minimax optimality property. When dimension q equals one, the confidence sets reduce to the usual Kolmogorov-Smirnov confidence bands, except that critical values are determined by bootstrapping.