SMALL-SAMPLE PROPERTIES OF SOME IMPROVED ESTIMATORS IN LOGISTIC REGRESSION MODEL WITH SKEW-NORMALLY DITRIBUTED EXPLANATORY VARIABLES.

summary This study explores the small-sample properties of five estimators (the unrestricted maximum likelihood estimator, the shrinkage restricted estimator, the shrinkage preliminary test estimator, the shrinkage estimator and the positiverule shrinkage estimator) using Monte Carlo experiments to confirm the asymptotic findings of Matin and Saleh (2005). It also explores the properties of test procedures (the Wald, the score and the likelihood ratio) in performing in estimators and tests under consideration. This study confirms the theoretical results in cases where comparisons are possible. When the number of explanatory variables is greater than or equal to 3 the shrinkage and the positive-rule shrinkage estimators always perform well. Considering the MSE the positive-rule shrinkage estimator performs better than the shrinkage estimator. The likelihood ratio test stands out to be the best. However, we lean toward the use of the Wald statistic when the problem of estimation is of paramount interest as it provides lower bias and MSE for the estimators.