An information criterion for parameters under a simple order restriction

Suppose we have independent random samples from each of k populations speci fied 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 con sider employing Akaike's information criterion (Akaike, 1973). However, the criterion is not appropriate for the order-restricted maximum likelihood e stimator of theta=(theta(1),...,theta(k)), since the normality or the asymp totic normality of the estimator is not valid. In this paper an information criterion is proposed for detecting the configuration of the true paramete rs with the simple order restriction. This method may also be applied for d etecting 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 norma l means satisfying the simple order restriction.