A Dimension-Reduction Approach for Generalized Linear Models

• Activity Number: 481
• Type: Invited
• Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
• Sponsor: International Chinese Statistical Association
• Author(s): Lixing Zhu*+
• Companies: Hong Kong Baptist University
• Keywords: quasi-likelihood ; Least squares ; Fisher information ; sparse model ; predictor selection

Abstract

Quasi-likelihood is one of the most popularly used methods for estimating parameters in generalized linear models with asymptotic efficiency. However, when the dimension of predictor vector is large, solutions of the corresponding estimating equations are unstable and even not convergent. This is clearly the case for sparse models in ``large p, small n" paradigms. In this paper, we propose a two-stage estimation approach. Different from classical quasi-likelihood, we first employ linear least squares for transformed response to obtain an estimation for a vector proportional to the parameter of interest. We then use quasi-likelihood to estimate one-dimensional scale of the parameter. As linear least squares is of a very simple closed form and is very efficient in computation, we can then efficiently reduce original dimension of predictor vector to one first so that we can efficiently apply quasi-likelihood to estimate scale of parameter. When the transformation for response is bounded, the new estimation is robust against distribution of error. The method is applied to predictor selection.