A Single Index Model with Varying Coefficients for Heterogeneous Data

• Activity Number: 477
• Type: Topic Contributed
• Date/Time: Wednesday, August 7, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Jianhui Zhou*+ and Feiyang Niu
• Companies: University of Virginia and University of Virginia
• Keywords: B-splines ; Canonical correlation ; Variable selection ; Single index model

Abstract

We study a single index model in which the coefficients in the index are allowed to vary with another covariate to accommodate data heterogeneity. An estimator of the varying coefficient functions is proposed through estimating a canonical correlation after implementing B-spline approximation. The proposed estimator avoids the direct estimation of the link function. We also develop a variable selection method in this single index model by penalizing the groups of B-spline coefficients. The asymptotic properties of the developed estimation and variable selection methods are investigated, and numerical studies are conducted to illustrate their performance. The developed methods can be further generalized to multi-index models for heterogeneous data, and are useful to study the effects of covariates for different subpopulations in many health studies.