Online Archive of University of Virginia Scholarship
Single-index Model with Varying coefficients686 views
Author
Niu, Feiyang, Statistics - Graduate School of Arts and Sciences, University of Virginia
Advisors
Zhou, Jianhui, Department of Statistics, University of Virginia
Abstract
To account for heterogeneity among subjects, we study a flexible single index model with varying coefficients. We consider using dimension reduction methods to estimate the varying coefficient functions. The developed method employs B-spline to approximate the varying coefficients and canonical correlation to estimate the B-spline coefficients, and avoids the direct estimation of the unknown link function. Due to the use of B-spline approximation, a group-wise Lasso penalty is imposed naturally on the estimator to select informative variables. A number of model selection criteria are applied and compared for tuning the parameter involved in group-wise Lasso penalty. The developed estimation and variable selection methods are easy to implement using the existing software packages, and can be generalized to multi-index models. Asymptotic properties are investigated, and simulation studies show satisfactory numerical performance of the developed methods. We apply the developed methods on a kidney study to select informative variable for survival time.
Degree
PHD (Doctor of Philosophy)
Keywords
Nonparametric; Single index model; Dimension reduction; Canonical correlation; B-spline
Language
English
Rights
All rights reserved (no additional license for public reuse)
Niu, Feiyang. Single-index Model with Varying coefficients. University of Virginia, Statistics - Graduate School of Arts and Sciences, PHD (Doctor of Philosophy), 2015-11-04, https://doi.org/10.18130/V3HK2K.