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Testing composite hypotheses

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

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Abstract

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.

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Published

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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