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Abstract: In this paper, we develop a new variable selection procedure for quantile varying coefficient models with longitudinal data. The proposed method is based on basis function approximation and a class of group versions of the adaptive LASSO penalty, which penalizes the norm of the within-group coefficients with . We show that with properly chosen adaptive group weights in the penalization, the resulting penalized estimators are consistent in variable selection, and the estimated functional coefficients retain the optimal convergence rate of nonparametric estimators under the true model. We assess the finite sample performance of the proposed procedure by an extensive simulation study, and the analysis of an AIDS data set and a yeast cell-cycle gene expression data set. [Copyright &y& Elsevier]