A first-order approximated jackknifed ridge estimator in binary logistic regression

Ozkale M. R., Arıcan E.

COMPUTATIONAL STATISTICS, vol.34, no.2, pp.683-712, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 34 Issue: 2
  • Publication Date: 2019
  • Doi Number: 10.1007/s00180-018-0851-6
  • Journal Name: COMPUTATIONAL STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.683-712
  • Keywords: Iteratively reweighted least squares, Ridge logistic estimator, Principal components logistic regression estimator, Multicollinearity, Receiving operating characteristic, Confidence interval
  • Çukurova University Affiliated: Yes

Abstract

The purpose of this paper is to solve the problem of multicollinearity that affects the estimation of logistic regression model by introducing first-order approximated jackknifed ridge logistic estimator which is more efficient than the first-order approximated maximum likelihood estimator and has smaller variance than the first-order approximated jackknife ridge logistic estimator. Comparisons of the first-order approximated jackknifed ridge logistic estimator to the first-order approximated maximum likelihood, first-order approximated ridge, first-order approximated r-k class and principal components logistic regression estimators according to the bias, covariance and mean square error criteria are done. Three different estimators for the ridge parameter are also proposed. A real data set is used to see the performance of the first-order approximated jackknifed ridge logistic estimator over the first-order approximated maximum likelihood, first-order approximated ridge logistic, first-order approximated r-k class and first-order approximated principal components logistic regression estimators. Finally, two simulation studies are conducted in order to show the performance of the first-order approximated jackknife ridge logistic estimator.