On sparse estimation for semiparametric linear transformation models

• Published in: Journal of multivariate analysis Vol. 101; no. 7; pp. 1594 - 1606
• Main Authors: Zhang, Hao Helen, Lu, Wenbin, Wang, Hansheng
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01.08.2010; Elsevier; Taylor & Francis LLC
• Series: Journal of Multivariate Analysis
• Subjects: Algorithms; Approximation; Asymptotic methods; Censored survival data; Censored survival data Linear transformation models LARS Shrinkage Variable selection; Distribution theory; Estimating techniques; Exact sciences and technology; Feature selection; LARS; Linear inference, regression; Linear transformation models; Mathematics; Multivariate analysis; Nonparametric inference; Parameter estimation; Probability and statistics; Sciences and techniques of general use; Shrinkage; Simulation; Statistics; Studies; Variable selection; secondary; LARS; Censored survival data; Linear transformation models; Shrinkage; primary; Variable selection; Ridge regression; Parameter estimation; secondary 62J07; Statistical distribution; Estimator robustness; primary 62N01; Non parametric estimation; Parametric model; Approximation algorithm; Multivariate analysis; Variable transformation; Linear model; Penalty method; Variance; Semiparametric model; Parametric method; Loss function; Consistent estimator; Approximation theory; Linear estimation; Survival data; Censored data; Covariance analysis; Model selection; Parametric estimation; Variance analysis; Statistical method; Statistical regression; Selection problem; Simulation; Asymptotic normality; Linear transformation; Estimating equation
• ISSN: 0047-259X; 1095-7243
• DOI: 10.1016/j.jmva.2010.01.015

Semiparametric linear transformation models have received much attention due to their high flexibility in modeling survival data. A useful estimating equation procedure was recently proposed by Chen et al. (2002)  [21] 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 has been 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.  [21], 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 a 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.