Some improved estimators in logistic regression model

The problem of estimating the parameters of logistic regression model is considered
when it is known from extraneous sources that the $\textit {uncertain prior information} in the form of the hypothesis$ H_0:\beta_0=\ldots, =\beta_{k-1}=\beta^0 $(pivot) may hold. Five estimators, namely, the unrestricted maximum likelihood estimator (UMLE), the shrinkage restricted estimator (SRE), the shrinkage preliminary test estimator (SPTE), the shrinkage estimator (SE) and the positive-rule shrinkage estimator (SE+) are considered. The SE and SE+ are the Stein-type estimators based on the preliminary test approach of Saleh and Sen. In the light of derived MSE matrices and distributional risks, the relative performance of the five estimators under local alternatives are studied in detail. These analyses reveal that when$ k \geq 3 $, we should use the SE or SE+ and for$ k \leq 2$ it is advisable to use the
preliminary test estimator (PTE).

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