Statistics and Data Science Seminar
Prof. Ejaz Ahmed
University of Michigan and University of Windsor
Lasso and Shrinkage Estimation in Generalized Linear Models
Abstract:
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 two 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 Haste type estimator (variant of lasso estimator) for generalized linear models. This comparison 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 real-life example showing the value of new method 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.
Wednesday April 30, 2008 at 3:30 PM in SEO 712