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 goof asymptotic properties. We show that the weighted likelihood can be derived from information-theoretic framework with the true distribution replaced with its empirical counterpart. However, in order to be effective, the weights involved in its construction need to judiciously chosen. We propose to choose the adaptive likelihood weights by using cross-validation. The asymptotic properties of the weighted likelihood estimator (WLE) with adaptive weights will be discussed in this talk. Results from simulation studies and application to disease mapping will also be presented.
Groupe d’études et de recherche en analyse des décisions