Speaker: Hossein Bevrani (Professor of Mathematical Statistics, Department of Statistics,Faculty of Mathematical sciences, University of Tabrizqui)
Title: Efficient Parameter Estimation in Generalized Linear Models
This talk considers the problem of estimation of the regression coefficients for the generalized linear models (GLMs) under multicollinearity situation. We propose non-penalty Stein-type shrinkage ridge estimation approach when it is conjectured that some prior information is available in the form of potential linear restrictions on the coefficients. We establish the asymptotic distributional biases and risks of the proposed estimators and investigate their relative performance with respect to the unrestricted ridge estimator. For comparison sake, we consider the two penalty estimators, namely, least absolute shrinkage and selection operator and Elastic-Net estimators and compare numerically their relative performance with the other listed estimators. The results are illustrated by two numerical examples and Monte-Carlo simulation studies are conducted with Poisson and Gamma response variables.