The Annals of Statistics

Confidence Sets for a Multivariate Distribution

R. Beran and P. W. Millar

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 14, Number 2 (1986), 431-443.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349931

Digital Object Identifier
doi:10.1214/aos/1176349931

Mathematical Reviews number (MathSciNet)
MR840507

Zentralblatt MATH identifier
0599.62057

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 62H12: Estimation

Keywords
Confidence set multivariate distribution affine invariance local asymptotic minimax bootstrap

Citation

Beran, R.; Millar, P. W. Confidence Sets for a Multivariate Distribution. Ann. Statist. 14 (1986), no. 2, 431--443. doi:10.1214/aos/1176349931. https://projecteuclid.org/euclid.aos/1176349931


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