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Minimum Φ-Divergence Estimator and Φ-Divergence Statistics in Generalized Linear Models with Binary Data

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Abstract

In this paper, we assume that the data are distributed according to a binomial distribution whose probabilities follow a generalized linear model. To fit the data the minimum φ-divergence estimator is studied as a generalization of the maximum likelihood estimator. We use the minimum φ-divergence estimator, which is the basis of some new statistics, for solving the problems of testing in a generalized linear model with binary data. A wide simulation study is carried out for studying the behavior of the new family of estimators as well as of the new family of test statistics.

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Authors and Affiliations

  1. Department of Statistics and O.R. (I), Complutense University of Madrid, Madrid, Spain

    J. A. Pardo & M. C. Pardo

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  1. J. A. Pardo
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  2. M. C. Pardo
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Correspondence to J. A. Pardo.

Additional information

This work was partially supported by Grant MTM2006-06872 and UCM2006-910707.

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Pardo, J.A., Pardo, M.C. Minimum Φ-Divergence Estimator and Φ-Divergence Statistics in Generalized Linear Models with Binary Data. Methodol Comput Appl Probab 10, 357–379 (2008). https://doi.org/10.1007/s11009-007-9054-2

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  • DOI: https://doi.org/10.1007/s11009-007-9054-2

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