Confidence Sets for a Multivariate Distribution

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.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.

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