Testing composite hypotheses; the Akaike-criterion revised

R. Moddemeijer

University of Groningen, Department of Computing Science,
P.O. Box 800, NL-9700 AV Groningen, The Netherlands,
phone: +31.50.363 3940 - fax: +31.50.363 38005 - e-mail: rudy@cs.rug.nl

Abstract

Akaike's criterion is often used to test composite hypotheses; for example to determine the order of a priori unknown Auto-Regressive and/or Moving Average models. Objections are formulated against Akaike's criterion and some modifications are proposed such that the criterion becomes consistent. A method is presented to test composite hypotheses given an upper-bound on the error of the first kind (Neyman-Pearson). For this purpose the method of maximum likelihood to estimate probability density functions (not parameters) is studied. As a result the single observation log likelihood is presented. The sequence of the single observation log likelihoods is a stochastic signal to which signal processing can be applied. This is a fruitful concept which opens a new field of research. The presented theory is verified by simulations.

Keywords

AIC, Akaike criterion, composite hypothesis, entropy, maximum likelihood, mutual information, Neyman-Pearson.

Published

Rejected for publication, no plans for publication, BibTeX

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