The complexity of semiparametric models poses new challenges to statisticalinference and model selection that frequently arise from real applications. Inthis work, we propose new estimation and variable selection procedures for thesemiparametric varying-coefficient partially linear model. We first studyquantile regression estimates for the nonparametric varying-coefficientfunctions and the parametric regression coefficients. To achieve niceefficiency properties, we further develop a semiparametric composite quantileregression procedure. We establish the asymptotic normality of proposedestimators for both the parametric and nonparametric parts and show that theestimators achieve the best convergence rate. Moreover, we show that theproposed method is much more efficient than the least-squares-based method formany non-normal errors and that it only loses a small amount of efficiency fornormal errors. In addition, it is shown that the loss in efficiency is at most11.1% for estimating varying coefficient functions and is no greater than 13.6%for estimating parametric components. To achieve sparsity with high-dimensionalcovariates, we propose adaptive penalization methods for variable selection inthe semiparametric varying-coefficient partially linear model and prove thatthe methods possess the oracle property. Extensive Monte Carlo simulationstudies are conducted to examine the finite-sample performance of the proposedprocedures. Finally, we apply the new methods to analyze the plasmabeta-carotene level data.
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