Restricted ridge estimator in generalized linear models: Monte Carlo simulation studies on Poisson and binomial distributed responses

KURTOĞLU F., Ozkale M. R.

COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, vol.48, no.4, pp.1191-1218, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 48 Issue: 4
  • Publication Date: 2019
  • Doi Number: 10.1080/03610918.2017.1408822
  • Journal Name: COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1191-1218
  • Keywords: Generalized linear models, Mean squared error, Multicollinearity, Poisson distribution, Restricted ridge estimation, REGRESSION, PARAMETERS
  • Çukurova University Affiliated: Yes

Abstract

It is known that collinearity among the explanatory variables in generalized linear models (GLMs) inflates the variance of maximum likelihood estimators. To overcome multicollinearity in GLMs, ordinary ridge estimator and restricted estimator were proposed. In this study, a restricted ridge estimator is introduced by unifying the ordinary ridge estimator and the restricted estimator in GLMs and its mean squared error (MSE) properties are discussed. The MSE comparisons are done in the context of first-order approximated estimators. The results are illustrated by a numerical example and two simulation studies are conducted with Poisson and binomial responses.