“Lasso and Shrinkage-type Estimation in Genralized Linear Models"

October 14, 2008
A Presentation by S. Ejaz Ahmed

We consider the estimation problem for the parameters of generalized linear models which may have a large collection of potential predictor variables and some of them may not have influence on the response of interest. In this situation, selecting the statistical model is always a challenging problem. In the context of several competing models, we demonstrate the relative performances of shrinkage and classical estimators based on the asymptotic analysis of quadratic risk functions. We demonstrate that the shrinkage estimator outperforms the maximum likelihood estimator uniformly. For comparison purpose, we also consider the Park and Hastie type estimator (variant of lasso estimator) for generalized linear models. Our simulation study shows that shrinkage method performs better than the lasso type estimation method when the dimension of the restricted parameter space is large. This talk ends with a real-life example showing the value of new methods in practice. More, specifically, we consider South African heart disease data, which was collected on males in a heart disease high-risk region of Western Cape, South Africa.

Ejaz Ahmed is Professor and Head of the Department of Mathematics and Statistics at the University of Windsor. He is a founding Director for Centre for Statistical Consulting, Research, Learning and Services (CSCRLS). He is the book review Editor of Technometrics. Dr. Ahmed serves as an Associate editor of several international statistical journals, including Computational Statistics and Data Analysis (CSDA) and Journal of Statistical Computation and Simulation (JSCS). He is also a guest co-editor for Linear Algebra and its Applications (LAA).


                                                                                  Harvey Qu giving Ejaz Ahmed a Certificate of Appreciation from the Detroit Chapter