On sparse estimation for semiparametric linear transformation models
AbstractSemiparametric 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 etÂ al. (2002)Â  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 etÂ al.Â , 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Multivariate Analysis.
Volume (Year): 101 (2010)
Issue (Month): 7 (August)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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- Hui Zou, 2008. "A note on path-based variable selection in the penalized proportional hazards model," Biometrika, Biometrika Trust, vol. 95(1), pages 241-247.
- Kani Chen, 2002. "Semiparametric analysis of transformation models with censored data," Biometrika, Biometrika Trust, vol. 89(3), pages 659-668, August.
- Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
- repec:cup:cbooks:9780521496032 is not listed on IDEAS
- Johnson, Brent A. & Lin, D.Y. & Zeng, Donglin, 2008. "Penalized Estimating Functions and Variable Selection in Semiparametric Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 672-680, June.
- Zeng, Donglin & Lin, D.Y., 2007. "Semiparametric Transformation Models With Random Effects for Recurrent Events," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 167-180, March.
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