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Biometrika 1999 86(1):141-152; doi:10.1093/biomet/86.1.141
© 1999 by Biometrika Trust
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An information criterion for parameters under a simple order restriction

K Anraku

Division of Childhood Education, Seinan Gakuin University, Fukuoka 814-8511, Japan anraku@seinan-gu.ac.jp

Suppose we have independent random samples from each of k populations specified by scalar-valued, unknown parameters {theta}1,...,{theta}k satisfying the simple order restriction {theta}1<=...<={theta}k. Our concern is to seek distinct parameters among {theta}1,...,{theta}k based on the data. To find a configuration of distinct parameters among the {theta}'s, one may consider employing Akaike's information criterion (Akaike, 1973). However, the criterion is not appropriate for the order-restricted maximum likelihood estimator of {theta}=({theta}1,...,{theta}k), since the normality or the asymptotic normality of the estimator is not valid. In this paper an information criterion is proposed for detecting the configuration of the true parameters with the simple order restriction. This method may also be applied for detecting a changepoint in a sequence of parameters with a monotone trend. A Monte Carlo study indicates that our new criterion is effective, compared to Akaike's information criterion, for detecting the configuration of normal means satisfying the simple order restriction.

Keywords:AIC; Changepoint; Information criterion; No-observed-adverse-effect level; Simple order restriction.


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