Automatic Smoothing Parameter Selection for Nonparametric Function Estimation with Clustered and Longitudinal Data

• Activity Number: 505
• Type: Topic Contributed
• Date/Time: Wednesday, August 4, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Jianhua Huang+ and Ganggang Xu*
• Companies: Texas A&M University and Texas A&M University
• Keywords: smoothing ; nonparametric function estimation

Abstract

While automatic smoothing parameter selection for nonparametric function estimation has been extensively researched for independent data, it is much less so for clustered and longitudinal data. Although leave-cluster(subject)-out cross-validation (CV) has been widely used, its theoretical property is unknown and its minimization is computationally expensive, especially when there are multiple smoothing parameters. In this paper, we show that leave cluster(subject)-out CV is optimal in that its minimization is asymptotically equivalent to the minimization of the empirical loss function. We develop an efficient algorithm to compute the smoothing parameters that minimize the CV criterion. Furthermore, we derive two simplifications of the leave-cluster(subject)-out CV, which are used to develop even more efficient algorithms for selecting the smoothing parameters.