Selecting likelihood weights by cross-validation

Details Selecting likelihood weights by cross-validation Selecting likelihood weights by cross-validation

2005-05-27

arxiv.org/abs/math/0505599v1

Annals of Statistics 2005, Vol. 33, No. 2, 463-500

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053604000001309 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053604000001309

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.

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