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

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 (...

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Bibliographic Details
Authors: Menéndez Calleja, María Luisa, Pardo Llorente, Leandro, Pardo Llorente, María del Carmen
Format: article
Publication Date:2008
Country:España
Institution:Universidad Complutense de Madrid (UCM)
Repository:Docta Complutense
Language:English
OAI Identifier:oai:docta.ucm.es:20.500.14352/50252
Online Access:https://hdl.handle.net/20.500.14352/50252
Access Level:Open access
Keyword:519.2
phi-divergence measures
Minimum phi-divergence estimator
phi-divergence statistics
Preliminary test estimator
Contiguous alternative hypotheses
Asymptotic bias
Asymptotic quadratic risk.
Estadística matemática (Matemáticas)
1209 Estadística
Description
Summary: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.