On sparse estimation for semiparametric linear transformation models

Hao Zhang, Wenbin Lu, Hansheng Wang

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1594-1606
Number of pages13
JournalJournal of Multivariate Analysis
Volume101
Issue number7
DOIs
StatePublished - Aug 2010
Externally publishedYes

Fingerprint

Linear Transformation Model
Linear transformations
Estimating Equation
Loss Function
Selection of Variables
Consistent Estimation
Entire Solution
Robust Estimators
Consistent Estimator
Survival Data
Term
Variable Selection
Shrinkage
Microarray Data
Regularity Conditions
High Efficiency
Penalty
Approximation Algorithms
Approximation algorithms
Microarrays

Keywords

  • Censored survival data
  • LARS
  • Linear transformation models
  • Shrinkage
  • Variable selection

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Numerical Analysis
  • Statistics and Probability

Cite this

On sparse estimation for semiparametric linear transformation models. / Zhang, Hao; Lu, Wenbin; Wang, Hansheng.

In: Journal of Multivariate Analysis, Vol. 101, No. 7, 08.2010, p. 1594-1606.

Research output: Contribution to journalArticle

Zhang, Hao ; Lu, Wenbin ; Wang, Hansheng. / On sparse estimation for semiparametric linear transformation models. In: Journal of Multivariate Analysis. 2010 ; Vol. 101, No. 7. pp. 1594-1606.
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