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

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 ϕ -divergence estimation ( M ϕ E ) , we consider some estimators for the parameters of the GLM: Unrestricted M ϕ E , restricted M ϕ E , Preliminary M ϕ E , Shrinkage M ϕ E , Shrinkage preliminary M ϕ E , James–Stein M ϕ E , Positive-part of Stein-Rule M ϕ E and Modified preliminary M ϕ 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.