Nonconcave penalized inverse regression in single-index models with high dimensional predictors
Journal of Multivariate Analysis
Nonconcave Penalized Likelihood With NP-Dimensionality
IEEE Transactions on Information Theory
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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.