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Selection of the best population: an information theoretic approach

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Menéndez Calleja, María Luisa and Pardo Llorente, Leandro and Tsairidis, Ch. and Zografos, Konstantinos (2003) Selection of the best population: an information theoretic approach. Metrika, 58 (2). pp. 117-147. ISSN 0026-1335

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Abstract

This paper is devoted to the statistical problem of ranking and selection populations by using the subset selection formulation. The interest is focused (i) on the selection of the best population among k independent populations and (ii) on the selection of the best population, which is closest to an additional standard or control population. With respect to the first problem the populations are ranked in terms of entropies of their distributions and the population whose distribution has maximum entropy is selected. For the second problem the populations are ranked in terms of divergences between their distributions and the distribution of the standard or control population and the population with the minimum divergence is selected. In each case the populations are assumed to have general parametric densities satisfying the classical regularity conditions of asymptotic statistic. Large sample properties of the estimators of entropies and divergences of the populations will be studied and used in order to determine the probabilities of correct selection of the proposed asymptotic selection rules. Illustrative examples, including a numerical example using real medical data appeared-in the literature; will be given for multivariate homoscedastic normal populations and populations described by the regular exponential family of distributions.


Item Type:Article
Uncontrolled Keywords:divergence; entropy; exponential family; Mahalanobis distance; multivariate normal distribution; ordering populations; selection of populations; subset selection approach;divergence; entropy.
Subjects:Sciences > Mathematics > Applied statistics
ID Code:17835
Deposited On:22 Jan 2013 12:24
Last Modified:26 Jul 2018 07:32

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