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

JOURNAL OF MULTIVARIATE ANALYSIS

卷:99

Article

Menendez, M. L.¹  Pardo, L.^2,3  Pardo, M. C.^2,3 

[1] Tech Univ Madrid, ETSAM, Dept Appl Math, Madrid, Spain

[2] Univ Complutense Madrid, Dept Stat, E-28040 Madrid, Spain

[3] Univ Complutense Madrid, OR I, E-28040 Madrid, Spain

关键词: phi-divergence measures;    Minimum phi-divergence estimator;    phi-divergence statistics;    Preliminary test estimator;    Contiguous alternative hypotheses;    Asymptotic bias;    Asymptotic quadratic risk;   

DOI  :  10.1016/j.jmva.2008.02.011

来源: Elsevier

【 摘 要 】

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. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

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