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Preliminary test estimators and phi-divergence measures in generalized linear models with binary data. (English) Zbl 1154.62051
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 \(\varphi\)-divergence estimation (\(M\varphi E\)), we consider some estimators for the parameters of the GLM: Unrestricted \(M\varphi E\), restricted \(M\varphi E\), Preliminary \(M\varphi E\), Shrinkage \(M\varphi E\), Shrinkage preliminary \(M\varphi E\), James-Stein \(M\varphi E\), Positive-part Stein-Rule \(M\varphi E\) and Modified preliminary \(M\varphi E\). The asymptotic bias as well as the 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.

MSC:
62J12 Generalized linear models (logistic models)
62F12 Asymptotic properties of parametric estimators
62F30 Parametric inference under constraints
62J07 Ridge regression; shrinkage estimators (Lasso)
62B10 Statistical aspects of information-theoretic topics
62H12 Estimation in multivariate analysis
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