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Shows JH, Lu W, Zhang HH. Sparse Estimation and Inference for Censored Median Regression. J Stat Plan Inference. 2010;140(7):1903-1917doi: 10.1016/j.jspi.2010.01.043.
Shows, J. H., Lu, W., & Zhang, H. H. (2010). Sparse Estimation and Inference for Censored Median Regression. Journal of statistical planning and inference, 140(7), 1903-1917. https://doi.org/10.1016/j.jspi.2010.01.043
Shows, Justin Hall, et al. "Sparse Estimation and Inference for Censored Median Regression." Journal of statistical planning and inference vol. 140,7 (2010): 1903-1917. doi: https://doi.org/10.1016/j.jspi.2010.01.043
Shows JH, Lu W, Zhang HH. Sparse Estimation and Inference for Censored Median Regression. J Stat Plan Inference. 2010 Jul;140(7):1903-1917. doi: 10.1016/j.jspi.2010.01.043. PMID: 20607110; PMCID: PMC2896027.
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J Stat Plan Inference. 2010 Jul;140(7):1903-1917. doi: 10.1016/j.jspi.2010.01.043.

Sparse Estimation and Inference for Censored Median Regression.

Journal of statistical planning and inference

Justin Hall Shows, Wenbin Lu, Hao Helen Zhang

Affiliations

  1. Department of Statistics, North Carolina State University, Raleigh, NC 27695, USA.

PMID: 20607110 PMCID: PMC2896027 DOI: 10.1016/j.jspi.2010.01.043

Abstract

Censored median regression has proved useful for analyzing survival data in complicated situations, say, when the variance is heteroscedastic or the data contain outliers. In this paper, we study the sparse estimation for censored median regression models, which is an important problem for high dimensional survival data analysis. In particular, a new procedure is proposed to minimize an inverse-censoring-probability weighted least absolute deviation loss subject to the adaptive LASSO penalty and result in a sparse and robust median estimator. We show that, with a proper choice of the tuning parameter, the procedure can identify the underlying sparse model consistently and has desired large-sample properties including root-n consistency and the asymptotic normality. The procedure also enjoys great advantages in computation, since its entire solution path can be obtained efficiently. Furthermore, we propose a resampling method to estimate the variance of the estimator. The performance of the procedure is illustrated by extensive simulations and two real data applications including one microarray gene expression survival data.

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