The Annals of Statistics

Loss Functions for Loss Estimation

Andrew L. Rukhin

Full-text: Open access

Abstract

A class of proper scoring functions which combine the error in a decision problem and the precision of the statistical decision rule is introduced. The Bayesian procedures with respect to these loss functions are pairs formed by the usual Bayes decision and by the expected posterior loss. A necessary and sufficient condition for admissibility under the corresponding risk is given.

Article information

Source
Ann. Statist., Volume 16, Number 3 (1988), 1262-1269.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350960

Digital Object Identifier
doi:10.1214/aos/1176350960

Mathematical Reviews number (MathSciNet)
MR959201

Zentralblatt MATH identifier
0672.62011

JSTOR
links.jstor.org

Subjects
Primary: 62C15: Admissibility
Secondary: 62A15 62C10: Bayesian problems; characterization of Bayes procedures

Keywords
Loss functions posterior risk admissibility concavity

Citation

Rukhin, Andrew L. Loss Functions for Loss Estimation. Ann. Statist. 16 (1988), no. 3, 1262--1269. doi:10.1214/aos/1176350960. https://projecteuclid.org/euclid.aos/1176350960


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