Variable selection for high-dimensional generalized varying-coefficient models

Abstract

In this paper, we consider the problem of variable selection for highdimensional generalized varying-coefficient models and propose a polynomial-spline based procedure that simultaneously eliminates irrelevant predictors and estimates the nonzero coefficients. In a "large p, small n" setting, we demonstrate the convergence rates of the estimator under suitable regularity assumptions. In particular, we show the adaptive group lasso estimator can correctly select important variables with probability approaching one and the convergence rates for the nonzero coefficients are the same as the oracle estimator (the estimator when the important variables are known before carrying out statistical analysis). To automatically choose the regularization parameters, we use the extended Bayesian information criterion (eBIC) that effectively controls the number of false positives. Monte Carlo simulations are conducted to examine the finite sample performance of the proposed procedures.

Estimation by polynomial splines with variable selection in additive Cox models

“…For example, Xie and Huang [4] studied variable selection in partially linear models; Wang et al [5], Wang and Xia [6], Wei et al [7] and Lian [8] investigated varying-coefficient models; Xue [9], Meier et al [10] and Huang et al [11] investigated additive models; and Li and Liang [12] and Wang et al [13] considered partially linear varying-coefficient models and partially linear additive models for variable selection on the linear part.…”

Nonparametric Independence Screening in Sparse Ultra-High-Dimensional Varying Coefficient Models

“…For the time-varying coefficient model, a special case of (1) with the exposure variable being the time t , Wang, Li and Huang (2008) applied the basis function approximations and the SCAD penalty to address the problem of variable selection. In the NP dimensional setting, Lian (2011) utilized the adaptive group Lasso penalty in time-varying coefficient models. These methods still face the aforementioned challenges of designing robust algorithm with reasonable computational cost while achieving statistical precision.…”

Variable Selection in Nonparametric and Semiparametric Regression Models

“…Like Lian (2010), Zhao and Xue propose to approximate  () by a linear combination of B-spline basis functions. Let…”