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.
"Confidence Sets for a Multivariate Distribution." Ann. Statist. 14 (2) 431 - 443, June, 1986. https://doi.org/10.1214/aos/1176349931