On Sparse Estimation for Semiparametric Linear Transformation Models

29 Pages Posted: 8 Feb 2010

See all articles by Hao Helen Zhang

Hao Helen Zhang

affiliation not provided to SSRN

Wenbin Lu

affiliation not provided to SSRN

Hansheng Wang

Peking University - Guanghua School of Management

Date Written: January 31, 2010

Abstract

Semiparametric linear transformation models have received much attention due to its high flexibility in modeling survival data. A useful estimating equation procedure was recently proposed by Chen et al. (2002) for linear transformation models to jointly estimate parametric and nonparametric terms. They showed that this procedure can yield a consistent and robust estimator. However, the problem of variable selection for linear transformation models is less studied, partially because a convenient loss function is not readily available under this context. In this paper, we propose a simple yet powerful approach to achieve both sparse and consistent estimation for linear transformation models. The main idea is to derive a profiled score from the estimating equation of Chen et al. (2002), construct a loss function based on the profile scored and its variance, and then minimize the loss subject to some shrinkage penalty. Under regularity conditions, we have shown that the resulting estimator is consistent for both model estimation and variable selection. Furthermore, the estimated parametric terms are asymptotically normal and can achieve higher efficiency than that yielded from the estimation equations. For computation, we suggest a one-step approximation algorithm which can take advantage of the LARS and build the entire solution path efficiently. Performance of the new procedure is illustrated through numerous simulations and real examples including one microarray data.

Keywords: Censored survival data, Linear transformation models, LARS, Shrinkage, Variable selection

JEL Classification: C00

Suggested Citation

Zhang, Hao Helen and Lu, Wenbin and Wang, Hansheng, On Sparse Estimation for Semiparametric Linear Transformation Models (January 31, 2010). Available at SSRN: https://ssrn.com/abstract=1545532 or http://dx.doi.org/10.2139/ssrn.1545532

Hao Helen Zhang

affiliation not provided to SSRN ( email )

Wenbin Lu

affiliation not provided to SSRN ( email )

Hansheng Wang (Contact Author)

Peking University - Guanghua School of Management ( email )

Peking University
Beijing, Beijing 100871
China

HOME PAGE: http://hansheng.gsm.pku.edu.cn

Register to save articles to
your library

Register

Paper statistics

Downloads
124
Abstract Views
1,089
rank
229,172
PlumX Metrics