The stochastic restricted ridge estimator in generalized linear models


Ozkale M. R. , Nyquist H.

STATISTICAL PAPERS, vol.62, no.3, pp.1421-1460, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 62 Issue: 3
  • Publication Date: 2021
  • Doi Number: 10.1007/s00362-019-01142-7
  • Title of Journal : STATISTICAL PAPERS
  • Page Numbers: pp.1421-1460
  • Keywords: Generalized linear models, Stochastic restrictions, Restricted estimation, Ridge regression, Sampling distribution, PRIOR INFORMATION, REGRESSION

Abstract

Many researchers have studied restricted estimation in the context of exact and stochastic restrictions in linear regression. Some ideas in linear regression, where the ridge and restricted estimations are the well known, were carried to the generalized linear models which provide a wide range of models, including logistic regression, Poisson regression, etc. This study considers the estimation of generalized linear models under stochastic restrictions on the parameters. Furthermore, the sampling distribution of the estimators under the stochastic restriction, the compatibility test and choice of the biasing parameter are given. A real data set is analyzed and simulation studies concerning Binomial and Poisson distributions are conducted. The results show that when stochastic restrictions and ridge idea are simultaneously applied to the estimation methods, the new estimator gains efficiency in terms of having smaller variance and mean square error.