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Stein-type estimation in logistic regression models based on minimum phi-divergence estimators

Menéndez Calleja, María Luisa and Pardo Llorente, Leandro and Pardo Llorente, María del Carmen (2009) Stein-type estimation in logistic regression models based on minimum phi-divergence estimators. Journal of the Korean Statistical Society, 38 (1). pp. 73-86. ISSN 1226-3192

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Abstract

In this paper we present a study of Stein-type estimators for the unknown parameters in logistic regression models when it is suspected that the parameters may be restricted to a subspace of the parameter space. The Stein-type estimators studied are based on the minimum phi-divergence estimator instead on the maximum likelihood estimator as well as on phi-divergence test statistics.

Item Type:Article
Uncontrolled Keywords:Logistic regression model; Phi-divergence test statistics; Minimum phi-divergence estimator; General linear hypotheses; Stein-type estimation; Statistics.
Subjects:Sciences > Mathematics > Applied statistics
ID Code:17392
References:

Ali, S. M., & Silvey, S. D. (1966). A general class of coefficients of divergence of one distribution from another. Journal of the Royal Statistical Society, Ser. B, 28, 131-142.

Baranchik, A. (1970). A family of minimax estimators of the mean of a multivariate normal distribution. Annals of Mathematical Statistics, 41, 642-645.

Berger, J. O. (1985). Statistical decision theory and Bayesian analysis (2nd ed.). New York: Springer-Verlag.

Cressie, N., & Pardo, L. (2002). In A. H. ElShaarawi, & W. W. Piegorich (Eds.), Encyclopedia of environmetrics: Vol. 3. Phi-divergence statistics (pp. 1551-1555). New York: John Wiley & Sons.

Cressie, N. A. C., Pardo, L., & Pardo, M. C. (2003). Size and power considerations for testing loglinear models using phi-divergence test statistics. Statistica Sinica, 13(2), 555-570.

Cressie, N., & Read, T. R. C. (1984). Multinomial goodness-of-fit tests. Journal of the Royal Statistical Society, Series B, 46, 440-464.

Csiszàr, I. (1963). Eine Informationstheorestiche Ungleichung und ihre Anwendung auf den Beweis der Ergodizität von Markoffschen Ketten. Publications of the mathematical Institute of Hungarian Academy of Sciences, Series A, 8, 84-108.

Efron, B., & Morris, C. (1973). Stein's estimation rule and its competitors. An empirical approach. Journal of the American Statistical Association, 68, 117-130.

Ghosh, M., Hwany, J., & Tsui, K. (1983). Construction of improved estimators in multiparameter estimation for discrete exponential families. Annals of Statistics, 11, 351-376. (Discussion by J.O. Berger, H. Malcolm Hudson and Carl Morris).

Hoffmann, K. (2000). Stein estimation: A review.Statistical Papers, 41, 127-158.

James, W., & Stein, C. (1961). Estimation with quadratic loss. In Proceedings of the fourth berkeley symposium on mathematical statistics and probability (pp. 361_379). Berkeley, CA: University of California Press.

Judge, G. G., & Bock, M. E. (1978). The statistical implications of pretest and stein-rule estimators in econometrics. Amsterdam: North Holland.

Liu, I., & Agresti, A. (2005). The analysis of ordered categorical data: An overview and a survey of recent developments. Test, 14(1), 1-73.

Menéndez, M. L., Pardo, J. A., & Pardo, L. (2008a). Phi-divergence test statistics for testing linear hypotheses in logistic regression models. Communications in Statistics (Theory and Methods), 37(4), 494-507.

Menéndez, M. L., Pardo, L., & Pardo, M. C. (2008b). Preliminary phi-divergence test estimators for linear restrictions in a logistic regression model. Statistical Papers.

Pardo, J. A., Pardo, L., & Pardo, M. C. (2005). Minimum phi-divergence estimator in logistic regression model. Statistical Papers, 47, 91-108.

Pardo, J. A., Pardo, L., & Pardo, M. C. (2006). Testing in logistic regression models based on phi-divergences measures. Journal of Statistical Planning and Inference, 132, 982-1006.

Pardo, L. (2006). Statistical inference based on divergence measures. New York: Chapman & Hall/CRC.

Saleh, A. K. Md. E. (2006). Theory of preliminary test and stein-type estimation with applications. Wiley.

Sen, P. K. (1986). On the asymptotic distributional risks of shrinkage and preliminary test versions of maximum likelihood estimators. Sankhya, Series A, 48, 354-371.

Stein, C. (1956). Inadmissibility of the usual estimator for the mean of a multivariate normal distribution. In Proceedings of the third berkeley symposium on mathematical statistics and probability, vol. 1 (pp. 197-206). Berkeley, CA: University of California Press.

Vajda, I. (1989). Theory of statistical inference and information. Dordrecht: Kluwer Academic.

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Last Modified:07 Feb 2014 09:46

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