Variable selection for high-dimensional generalized varying-coefficient models

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.