On tests of independence based on minimum φ-divergence estimator with constraints: An application to modeling DNA

Authors:
M. L. Menéndez;J. A. Pardo;L. Pardo;K. Zografos
Affiliations:
Department of Applied Mathematics, Polytechnical University of Madrid, 28040 Madrid, Spain;Department of Statistics and O.R., Complutense University of Madrid, 28040 Madrid, Spain;Department of Statistics and O.R., Complutense University of Madrid, 28040 Madrid, Spain;Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece
Venue:
Computational Statistics & Data Analysis
Year:
2006

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Abstract

A new family of estimators, Minimum @f-divergence estimators, is introduced for the problem of independence in a two-way contingency table and their asymptotic properties are studied. Based on this new family of estimators, a new family of test statistics for the problem of independence is defined. This new family of test statistics yield the likelihood ratio test and the Pearson test statistic as special cases. A simulation study is presented to show that some new test statistics offer an attractive alternative to the classical Pearson and likelihood ratio test statistics for this problem. The procedures proposed in this paper can be used for testing positional independence of a DNA sequence as it is illustrated by a numerical example.