  Ultra-high dimensional longitudinal data are increasingly common and the
analysis is challenging both theoretically and methodologically. We offer a new
automatic procedure for finding a sparse semivarying coefficient model, which
is widely accepted for longitudinal data analysis. Our proposed method first
reduces the number of covariates to a moderate order by employing a screening
procedure, and then identifies both the varying and constant coefficients using
a group SCAD estimator, which is subsequently refined by accounting for the
within-subject correlation. The screening procedure is based on working
independence and B-spline marginal models. Under weaker conditions than those
in the literature, we show that with high probability only irrelevant variables
will be screened out, and the number of selected variables can be bounded by a
moderate order. This allows the desirable sparsity and oracle properties of the
subsequent structure identification step. Note that existing methods require
some kind of iterative screening in order to achieve this, thus they demand
heavy computational effort and consistency is not guaranteed. The refined
semivarying coefficient model employs profile least squares, local linear
smoothing and nonparametric covariance estimation, and is semiparametric
efficient. We also suggest ways to implement the proposed methods, and to
select the tuning parameters. An extensive simulation study is summarized to
demonstrate its finite sample performance and the yeast cell cycle data is
analyzed.
