The Annals of Statistics
- Ann. Statist.
- Volume 19, Number 2 (1991), 935-951.
Minimaxity of the Empirical Distribution Function in Invariant Estimation
Qiqing Yu and Mo-suk Chow
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
