SOME IMPROVED ESTIMATORS IN LOGISTIC REGRESSION MODEL
Keywords:
Preliminary test estimator, Shrinkage estimator, Steintype estimator, Quadratic risk, Pitman alternatives, Wald test. AMS Classification, 62Jxx.Abstract
The problem of estimating the parameters of logistic regression model is considered
when it is known from extraneous sources that the uncertain prior information
in the form of the hypothesis H0 : 0 = . . . = k−1 = 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 3, we should use the SE or SE+ and for k 2 it is advisable to use the
preliminary test estimator (PTE).
