Estimation for the Power-transformed Varying-coefficient Quantile Regression Model

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In this article, we consider the varying-coefficient quantile regression model with a power transformation on the dependent variable. The functional coefficients are estimated by the use of B-spline and the number of knots is chosen according to Schwarz-type Information Criterion. The transformation parameter is estimated by minimizing the cusum residual square sum. We show that the estimates of transformation parameter and the functional coefficients are consistent, and also obtain the rates of convergence of the estimation of functional coefficients. The proposed methods are illustrated by some simulated studies and a real data example.