ESTIMATING A MODEL THROUGH THE CONDITIONAL MLE

TAKEMI YANAGIMOTO

The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106, Japan

(Received September 26, 1989; revised July 30, 1990)

Abstract. The estimation problem of a model through the conditional maximum likelihood estimator (MLE) is explored. The estimated model is compared using the two dual Kullback-Leibler losses with that through the unconditional MLE. The former is found to be superior to the latter under familiar models. This result is applicable to the model selection problem. These suggest a novel extensive use of the conditional likelihood, since the traditional use of the conditional likelihood was restricted only on inference for the structural parameter.

Key words and phrases: AIC, conditional inference, exponential family, Kullback-Leibler loss, model selection.