Nonparametric varying-coefficient models are commonly used for analysis of data measured repeatedly over time, including longitudinal and functional responses data. While many procedures have been developed for estimating the varying-coefficients, the problem of variable selection for such models has not been addressed. In this article, we present a regularized estimation procedure for variable selection for such nonparametric varying-coefficient models using basis function approximations and a group smoothly clipped absolute deviation penalty (gSCAD). This gSCAD procedure simultaneously selects significant variables with time-varying effects and estimates unknown smooth functions using basis function approximations. With appropriate selection of the tuning parameters, we have established the oracle property of the procedure and the consistency of the function estimation. The methods are illustrated with simulations and an application to analysis of microarray time-course gene expression data to in order to identify the transcription factors that are related to yeast cell cycle process.



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