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

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  • J. A. Pardo

    (Complutense University of Madrid)

  • M. C. Pardo

    (Complutense University of Madrid)

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.

Suggested Citation

  • J. A. Pardo & M. C. Pardo, 2008. "Minimum Φ-Divergence Estimator and Φ-Divergence Statistics in Generalized Linear Models with Binary Data," Methodology and Computing in Applied Probability, Springer, vol. 10(3), pages 357-379, September.
    • Handle: RePEc:spr:metcap:v:10:y:2008:i:3:d:10.1007_s11009-007-9054-2
    DOI: 10.1007/s11009-007-9054-2
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    References listed on IDEAS

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    1. Konstantinos Fokianos, 2002. "Power Divergence Family of Tests for Categorical Time Series Models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(3), pages 543-564, September.
    2. Pardo, M. C., 1999. "On Burbea-Rao Divergence Based Goodness-of-Fit Tests for Multinomial Models," Journal of Multivariate Analysis, Elsevier, vol. 69(1), pages 65-87, April.
    3. Morales, D. & Pardo, L. & Vajda, I., 1997. "Some New Statistics for Testing Hypotheses in Parametric Models, ," Journal of Multivariate Analysis, Elsevier, vol. 62(1), pages 137-168, July.
    4. Munoz-Garcia, J. & Munoz-Pichardo, J.M. & Pardo, L., 2006. "Cressie and Read power-divergences as influence measures for logistic regression models," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3199-3221, July.
    5. M.L. Menéndez & J.A. Pardo & L. Pardo, 2003. "Theory & Methods: Tests for Bivariate Symmetry Against Ordered Alternatives in Square Contingency Tables," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 45(1), pages 115-123, March.
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