Local Weighted Composite Quantile Estimating for Varying Coefficient Models

A generalization of classical linear models is varying coefficientmodels, which offer a flexible approach to modeling nonlinearity between covariates. Amethod of local weighted composite quantile regression is suggested to estimate thecoefficient functions. The local Bahadur representation of the local estimator is derivedand the asymptotic normality of the resulting estimator is established. Comparing to thelocal least squares estimator, the asymptotic relative efficiency is examined for the localweighted composite quantile estimator. Both theoretical analysis and numerical simulationsreveal that the local weighted composite quantile estimator can obtain more efficient thanthe local least squares estimator for various non-normal errors. In the normal error case,the local weighted composite quantile estimator is almost as efficient as the local leastsquares estimator. Monte Carlo results are consistent with our theoretical findings. Anempirical application demonstrates the potential of the proposed method.