SCAD-penalized regression in additive partially linear proportional hazards models with an ultra-high-dimensional linear part

Heng Lian, Jianbo Li and Xingyu Tang

Journal of Multivariate Analysis, 2014, vol. 125, issue C, 50-64

Abstract: We consider the problem of simultaneous variable selection and estimation in additive partially linear Cox’s proportional hazards models with high-dimensional or ultra-high-dimensional covariates in the linear part. Under the sparse model assumption, we apply the smoothly clipped absolute deviation (SCAD) penalty to select the significant covariates in the linear part and use polynomial splines to estimate the nonparametric additive component functions. The oracle property of the estimator is demonstrated, in the sense that consistency in terms of variable selection can be achieved and that the nonzero coefficients are asymptotically normal with the same asymptotic variance as they would have if the zero coefficients were known a priori. Monte Carlo studies are presented to illustrate the behavior of the estimator using various tuning parameter selectors.

Keywords: Akaike information criterion (AIC); Bayesian information criterion (BIC); Extended Bayesian information criterion (EBIC); Cross-validation; Ultra-high dimensional regression; SCAD (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.jmva.2013.12.002

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