The Annals of Statistics

Minimaxity of the Empirical Distribution Function in Invariant Estimation

Qiqing Yu and Mo-suk Chow

Full-text: Open access

Abstract

Consider the problem of continuous invariant estimation of a distribution function with the weighted Cramer-von Mises loss. The minimaxity of the empirical distribution function, which is also the best invariant estimator, is proved for any sample size. This solves a long-standing conjecture.

Article information

Source
Ann. Statist., Volume 19, Number 2 (1991), 935-951.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348129

Digital Object Identifier
doi:10.1214/aos/1176348129

Mathematical Reviews number (MathSciNet)
MR1105853

Zentralblatt MATH identifier
0739.62011

JSTOR
links.jstor.org

Subjects
Primary: 62C15: Admissibility
Secondary: 62D05: Sampling theory, sample surveys

Keywords
Minimaxity within a class Cramer-von Mises loss invariant estimator nonparametric estimator Egoroff's theorem Baire category theorem product measure

Citation

Yu, Qiqing; Chow, Mo-suk. Minimaxity of the Empirical Distribution Function in Invariant Estimation. Ann. Statist. 19 (1991), no. 2, 935--951. doi:10.1214/aos/1176348129. https://projecteuclid.org/euclid.aos/1176348129


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