Additive Partially Linear Regression

• Activity Number: 303
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Fengrong Wei*+
• Companies: University of West Georgia
• Keywords: semiparametric ; Lasso ; consistency

Abstract

The problem of simultaneous variable selection and estimation in partially linear additive models with a large number of grouped variables in the linear part and a large number of nonparametric components will be considered. In the problem, the number of grouped variables may be larger than the sample size, but the number of important groups is ``small'' relative to the sample size. The adaptive group Lasso is applied to select the important groups, using spline bases to approximate the nonparametric components and the group Lasso is applied to obtain an initial consistent estimator. Under appropriate conditions, it is shown that, the group Lasso selects the number of groups which is comparable with the underlying important groups and is estimation consistent, the adaptive group Lasso selects the correct important groups with probability converging to one as the sample size increases and is selection consistent. The results of simulation studies show that the adaptive group Lasso procedure works well with samples of moderate size.