The Annals of Statistics

Selecting likelihood weights by cross-validation

Xiaogang Wang and James V. Zidek

Full-text: Open access

Abstract

The (relevance) weighted likelihood was introduced to formally embrace a variety of statistical procedures that trade bias for precision. Unlike its classical counterpart, the weighted likelihood combines all relevant information while inheriting many of its desirable features including good asymptotic properties. However, in order to be effective, the weights involved in its construction need to be judiciously chosen. Choosing those weights is the subject of this article in which we demonstrate the use of cross-validation. We prove the resulting weighted likelihood estimator (WLE) to be weakly consistent and asymptotically normal. An application to disease mapping data is demonstrated.

Article information

Source
Ann. Statist., Volume 33, Number 2 (2005), 463-500.

Dates
First available in Project Euclid: 26 May 2005

Permanent link to this document
https://projecteuclid.org/euclid.aos/1117114325

Digital Object Identifier
doi:10.1214/009053604000001309

Mathematical Reviews number (MathSciNet)
MR2163148

Zentralblatt MATH identifier
1068.62025

Subjects
Primary: 62F10: Point estimation 62H12: Estimation

Keywords
Asymptotic normality consistency cross-validation weighted likelihood

Citation

Wang, Xiaogang; Zidek, James V. Selecting likelihood weights by cross-validation. Ann. Statist. 33 (2005), no. 2, 463--500. doi:10.1214/009053604000001309. https://projecteuclid.org/euclid.aos/1117114325


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