Confidence Sets for a Multivariate Distribution

R. Beran; P. W. Millar

doi:10.1214/aos/1176349931

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Home > Journals > Ann. Statist. > Volume 14 > Issue 2 > Article

June, 1986 Confidence Sets for a Multivariate Distribution

R. Beran, P. W. Millar

Ann. Statist. 14(2): 431-443 (June, 1986). DOI: 10.1214/aos/1176349931

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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.

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