#
Testing composite hypotheses; the Akaike-criterion revised

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

University of Groningen, Department of Computing Science,
Groningen,
Computing Science Report: CS-R9707,
BibTeX

#### Related work

other publications