IMPROVED ESTIMATION OF THE EXPECTED KULLBACK-LEIBLER DISCREPANCY IN CASE OF MISSPECIFICATION

In case of misspecificalion, theAkaikc information criterion (AIC;Akaike, 1973, in Petrov & Csaki, eds., Second international Symposium on Information Theory, pp. 267-281. Budapest: Akademia Kiado) is an asymplotically biased estimator of the expected Kullback-Leibler discrepancy. This paper gives simple expressions for the bias that can be used to construct improved estimators. However, for the examples that are considered in detail it turns out that model selection procedures based on such improved estimators are nearly equivalent to model selection procedures based on severely biased estimators.