Small-sample properties of some improved estimators in logistic regression with skew-normally distributed explanatory variables

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.