Global and Local Functional Sparsity in Nonparametric Regression

• Activity Number: 322
• Type: Topic Contributed
• Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Haonan Wang*+ and Yan Tu and Bo Kai
• Companies: Colorado State University and Colorado State University and College of Charleston
• Keywords: model selection ; smoothing ; sparsity

Abstract

In this talk, we consider the problem of estimation and selection in nonparametric regression. The notion of functional sparsity is introduced as a generalization of parameter sparsity in classical parametric regression model. In particular, two different types of sparsity are of interest, including both global sparsity and local sparsity. The goal is to produce a sparse estimate which assigns zero values over regions where the true underlying function is zero. Most classical smoothing techniques yield consistent estimates with no sparsity. Here, a penalized approach is proposed for simultaneous functional estimation and model selection. Asymptotic properties of the procedure, including both consistency in estimation and sparsity in model selection, are established. This approach is also implemented to varying coefficient model and functional dynamic model. The methodology is illustrated through simulation studies and real data analysis.