A jackknifed ridge estimator in probit regression model

Abstract

In this study, the effects of multicollinearity on the maximum likelihood estimator are analyzed in the probit regression model. It is known that the near-linear dependencies in the design matrix affect the maximum likelihood estimation negatively, namely, the standard errors become so large so that the estimations are said to be inconsistent. Therefore, a new jackknifed ridge estimator is introduced as an alternative to the maximum likelihood technique and the well-known ridge estimator. The mean squared error properties of the listed estimators are investigated theoretically. In order to evaluate the performance of the estimators, a Monte Carlo simulation study is designed, and simulated mean squared error and squared bias are used as performance criteria. Finally, the benefits of the new estimator are illustrated via a real data application.

Keywords:

• Multicollinearity
• ridge estimator
• jackknifed ridge estimator
• probit model
• mean squared error

2010 AMS Mathematics Subject Classifications:

• 62J05
• 62J07

Disclosure statement

No potential conflict of interest was reported by the author(s).