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Preliminary test estimators and phi-divergence measures in generalized linear models with binary data

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Menéndez Calleja, María Luisa and Pardo Llorente, Leandro and Pardo Llorente, María del Carmen (2008) Preliminary test estimators and phi-divergence measures in generalized linear models with binary data. Journal of multivariate analysis, 99 (10). pp. 2265-2284. ISSN 0047-259X

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Official URL: http://www.sciencedirect.com/science/article/pii/S0047259X08000547


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Abstract

We consider the problem of estimation of the parameters in Generalized Linear Models (GLM) with binary data when it is suspected that the parameter vector obeys some exact linear restrictions which are linearly independent with some degree of uncertainty. Based on minimum phi-divergence estimation (M phi E), we consider some estimators for the parameters of the GLM: Unrestricted M phi E, restricted M phi E, Preliminary M phi E, Shrinkage M phi E, Shrinkage preliminary M phi E, James-Stein M phi E, Positive-part of Stein-Rule M phi E and Modified preliminary M phi E. Asymptotic bias as well as risk with a quadratic loss function are studied under contiguous alternative hypotheses. Some discussion about dominance among the estimators studied is presented. Finally, a simulation study is carried out.


Item Type:Article
Uncontrolled Keywords:phi-divergence measures; Minimum phi-divergence estimator; phi-divergence statistics; Preliminary test estimator; Contiguous alternative hypotheses; Asymptotic bias; Asymptotic quadratic risk.
Subjects:Sciences > Mathematics > Mathematical statistics
ID Code:17532
Deposited On:21 Dec 2012 11:28
Last Modified:26 Feb 2015 09:10

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