Asymptotic Optimality of Crossvalidation Methods in Prediction and Likelihood Inference

• Activity Number: 351
• Type: Invited
• Date/Time: Wednesday, August 6, 2003 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Mark Vanderlaan*+
• Companies: University of California
• Keywords: likelihood crossvalidation ; variable selection ; model selection ; prediction ; double robust estimation ; censored data

Abstract

Likelihood based crossvalidation is a statistical tool for selecting a density estimate based on n i.i.d. observations from the true density among a collection of candidate density estimators. General examples are the selection of a model indexing a maximum likelihood estimate, and prediction with L2 loss function. In this article we establish asymptotic optimality of a general class of likelihood based crossvalidation procedures (as indexed by the type of sample splitting used, e.g. V-fold crossvalidation) in the sense that it performs asymptotically as well as an optimal benchmark model selector which depends on the true density. We illustrate these asymptotic results and the practical performance of likelihood based crossvalidation for the purpose of bandwidth selection and variable selection. We also provide the generalizations of these methods to censored data, using locally efficient doubly robust risk estimators based on the validation sample. We illustrate their applications in prediction of survival based on gene expression data, detection of binding sites in the genome based on gene expression data and sequence data.