Semiparametric Model Pursuit

• Activity Number: 560
• Type: Invited
• Date/Time: Wednesday, August 4, 2010 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Jian Huang*+
• Companies: The University of Iowa
• Keywords: Partially linear model ; penalized least squares ; model pursuit consistency ; large p small n ; sparse model ; efficiency

Abstract

In standard semiparametric partially linear models, the linear and nonparametric components are specified prior to data analysis. However, in practice, it is usually difficult to make such specification. We propose a penalized approach for determining which components can take the linear form and which components should be modeled nonparametrically. We call the proposed approach semiparametric model pursuit. We show that this approach is model pursuit consistent if the underlying model is indeed a partially linear model, in the sense that it can identify the correct model with probability converging to one. We also show that the proposed approach yields an estimator that is semiparametrically efficient. Our approach and results are applicable when the number of variables is larger than the sample size when a sparseness condition is assumed.