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2005•Journal of Statistical ResearchOpen access

SOME IMPROVED ESTIMATORS IN LOGISTIC REGRESSION MODEL

M. A. Matin, A. K. Md. Ehsanes Saleh

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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).

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What this paper is about

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).

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Available 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).

Key concepts: Estimator, Shrinkage estimator, Statistics, Mathematics, Shrinkage, Logistic regression, James–Stein estimator, Econometrics

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