Improved ridge regression estimators for the logistic regression model

Authors:
A. K. Saleh;B. M. Kibria
Affiliations:
School of Mathematics and Statistics, Carleton University, Ottawa, Canada K1S 5B6;Department of Mathematics and Statistics, Florida International University, Miami, USA 33199
Venue:
Computational Statistics
Year:
2013

Citing 3
Cited 0

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Abstract

The estimation of the regression parameters for the ill-conditioned logistic regression model is considered in this paper. We proposed five ridge regression (RR) estimators, namely, unrestricted RR, restricted ridge regression, preliminary test RR, shrinkage ridge regression and positive rule RR estimators for estimating the parameters $$(\beta )$$ when it is suspected that the parameter $$\beta $$ may belong to a linear subspace defined by $$H\beta =h$$. Asymptotic properties of the estimators are studied with respect to quadratic risks. The performances of the proposed estimators are compared based on the quadratic bias and risk functions under both null and alternative hypotheses, which specify certain restrictions on the regression parameters. The conditions of superiority of the proposed estimators for departure and ridge parameters are given. Some graphical representations and efficiency analysis have been presented which support the findings of the paper.