A new biased estimator in logistic regression model

Abstract

In this paper, the $r-k$ class logistic estimator which combines the ridge logistic and principal components logistic regression (PCLR) estimators is proposed. The comparisons of the $r-k$ class logistic, ridge logistic and PCLR estimators to the maximum likelihood (ML) estimator according to the asymptotic matrix mean square error (MSE) criterion and the comparisons of the $r-k$ class logistic estimator to the ML, PCLR and ridge logistic estimators in the sense of asymptotic scalar MSE criterion are done. The results are illustrated with numerical examples and a simulation study is done.

Keywords:

• maximum likelihood estimator
• ridge logistic estimator
• principal components logistic regression estimator
• multicollinearity
• binary data

AMS Subject Classifications:

• 62J07
• 62J12

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. The bold values in Tables 4–15 show the minimum EMSE values.