Testing composite hypotheses

R. Moddemeijer and E.W. Gröneveld

University of Twente, Department of Electrical Engineering,
P.O. Box 217, NL-7500 AE Enschede, The Netherlands,

present addres

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


We consider the estimation of parameters of a probability density function (pdf) of the observed vector variable Z or rather the selection of one pdf from an a priori defined set of hpothetical pdf's of Z. It is assumed that the set set consistes of two subsets of pdf's f0(Z;P) and f1(Z;Q), P and Q are vectors of continuous parameters. The test of f1 versus f0 is then a test of composite hypotheses. The optimal parameters are P* and Q* maximizing the expectation of log f0(Z;P) and log f1(Z;Q). The subset in which this maximum is the largest is the subset to be selected. For a test based on N observations we replace the expectation by the average; this average suffers from an N-dependent bias. We discuss ist (over)compensation. We relate it to the Akaike Information theoretic Criterion (AIC) and suggest an improved test to replace the latter.


Tenth Symposium on Information Theory in the Benelux, May 25-26, 1989, Houthalen, Belgium, pp. 133-138, Ed. Barbé, A.M., Werkgemeenschap Informatie- en Communicatietheorie, Enschede, ISBN 90-71048-05-5, BibTeX
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