Nonparametric Independence Screening and Structural Identification for Ultra-High-Dimensional Longitudinal Data

• Activity Number: 544
• Type: Topic Contributed
• Date/Time: Wednesday, August 6, 2014 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Toshio Honda*+ and Ming-Yen Cheng and Jialiang Li and Heng Peng
• Companies: Hitotsubashi University and National Taiwan University and National University of Singapore and Hong Kong Baptist University
• Keywords: marginal model ; semivarying coefficient model ; B-spline ; SCAD ; sparsity ; oracle property

Abstract

Ultra-high dimensional longitudinal data are increasingly common and the analysis is challenging. We offer a new automatic procedure in hunting for a sparse semivarying coefficient model. Our proposed method first reduces the number of covariates to a moderate order by employing a screening procedure, and then identifies both the varying and non-zero constant coefficients using a group SCAD estimator, which is then refined by accounting for the within-subject correlation. Under weaker conditions than those in the literature, we show that with high probability only irrelevant variables will be screened out and the number of variables left can be bounded by a moderate order, thus the desirable properties of the subsequent variable selection step is allowed. Our group SCAD estimator also detects the non-zero constant and varying effects simultaneously. The refined semivarying coefficient model employs profile least squares, local linear smoothing and nonparametric covariance estimation, and is semiparametric efficient. We also suggest ways to implement the method and to select the tuning parameters and the smoothing parameters. We also carried out simulation studies and data analysis.