The Annals of Statistics

Selecting likelihood weights by cross-validation

Xiaogang Wang and James V. Zidek

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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

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

First available in Project Euclid: 26 May 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F10: Point estimation 62H12: Estimation

Asymptotic normality consistency cross-validation weighted likelihood


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

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