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