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A preliminary test in classification and probabilities of misclassification

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Menéndez, María Luisa and Pardo Llorente, Julio Ángel and Pardo Llorente, Leandro and Zografos, Konstantinos (2005) A preliminary test in classification and probabilities of misclassification. Statistics, 39 (3). pp. 183-205. ISSN 0233-1888

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Official URL: http://www.tandfonline.com/doi/pdf/10.1080/02331880500097986


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Abstract

Consider f(theta) to be a probability density function with parameter theta. A set of k populations can now be defined such that the ith population Pi(i) is the set of density functions f(theta 1(i)),...,f(theta mi(i)). This paper proposes a test, based on the Psi-dissimilariiy, of the hypothesis that a new individual from a population Pi(0) with a density function f(theta 0), belongs to the ith population. The probabilities of misclassification of the minimum Psi-dissimilarity classification rule are also obtained. In this paper, it is assumed that the parameters theta(1)((i)),...,theta(mi)((i)) and may be theta(0) are unknown and must be estimated from a set of training samples. Explicit expressions for the hypothesis test and the probabilities of misclassification are derived for the case where the populations Pi(i) consist of homoscedastic normal, as well as for gamma distributions.


Item Type:Article
Uncontrolled Keywords:Classification; Discrimination; Minimum distance classification rule; Probabilities of misclassification; ϕ-Dissimilarity, φ-Divergence
Subjects:Sciences > Mathematics > Mathematical statistics
ID Code:17495
Deposited On:20 Dec 2012 10:53
Last Modified:26 Jul 2018 07:09

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