Variable selection in Cox regression models with varying coefficients. (English) Zbl 1432.62338
Summary: We deal with Cox regression models with varying coefficients. We concentrate on time-varying coefficient models and give a brief comment on another kind of varying coefficient models. When we have \(p\)-dimensional covariates and \(p\) increases with the sample size, it is often the case that only a small part of the covariates are relevant. Therefore we consider 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 \(L_2\) convergence rate, the sparsity, and the oracle property. Simulation studies and a real data analysis show the performance of these procedures.
MSC:
| 62N02 | Estimation in survival analysis and censored data |
| 62G08 | Nonparametric regression and quantile regression |
| 62J07 | Ridge regression; shrinkage estimators (Lasso) |
| 62G20 | Asymptotic properties of nonparametric inference |
| 62-08 | Computational methods for problems pertaining to statistics |
Keywords:
high-dimensional data; sparsity; oracle estimator; B-splines; group SCAD; adaptive group Lasso; \(L_2\) convergence rateReferences:
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