Statistica Sinica 22 (2012), 1563-1588
doi:http://dx.doi.org/10.5705/ss.2010.308
VARIABLE SELECTION
FOR HIGH-DIMENSIONAL
GENERALIZED VARYING-COEFFICIENT MODELS
Heng Lian
Nanyang Technological University
Abstract: In this paper, we consider the problem of
variable selection for high-dimensional generalized
varying-coefficient models and propose a polynomial-spline based
procedure that simultaneously eliminates irrelevant predictors and
estimates the nonzero coefficients. In a ``large 
, small 
"
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.
Key words and phrases: Diverging parameters, group lasso,
polynomial splines, quasi-likelihood.