Variable selection in Cox regression models with varying coefficients

Toshio Honda and Wolfgang Härdle

No 2012-061, SFB 649 Discussion Papers from Humboldt University Berlin, Collaborative Research Center 649: Economic Risk

Abstract: We deal with two kinds of Cox regression models with varying coefficients. The coefficients vary with time in one model. In the other model, there is an important random variable called an index variable and the coefficients vary with the variable. In both models, we have p-dimensional covariates and p increases moderately. However, it is the case that only a small part of the covariates are relevant in these situations. We carry out variable selection and estimation of the coefficient functions by using the group SCAD-type estimator and the adaptive group Lasso estimator. We examine the theoretical properties of the estimators, especially the L2 convergence rate, the sparsity, and the oracle property. Simulation studies and a real data analysis show the performance of these new techniques.

Keywords: Cox regression model; high-dimensional data; sparsity; oracle estimator; B-splines; group SCAD; adaptive group Lasso; L2 convergence rate (search for similar items in EconPapers)
JEL-codes: C14 C24 (search for similar items in EconPapers)
Date: 2012
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