  This paper proposes a new robust smooth-threshold estimating equation to
select important variables and automatically estimate parameters for high
dimensional longitudinal data. A novel working correlation matrix is proposed
to capture correlations within the same subject. The proposed procedure works
well when the number of covariates p increases as the number of subjects n
increases. The proposed estimates are competitive with the estimates obtained
with the true correlation structure, especially when the data are contaminated.
Moreover, the proposed method is robust against outliers in the response
variables and/or covariates. Furthermore, the oracle properties for robust
smooth-threshold estimating equations under "large n, diverging p" are
established under some regularity conditions. Extensive simulation studies and
a yeast cell cycle data are used to evaluate the performance of the proposed
method, and results show that our proposed method is competitive with existing
robust variable selection procedures.
