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TITLE: Local Composite Quantile Regression
SPEAKER: Professor Runze Li
ABSTRACT:
Local polynomial regression is a useful nonparametric regression tool to explore fine data structures ad has been widely used in practice. In this paper, we propose a new nonparametric regression technique called local composite quantile (CQR) smoothing in order to further improve the local polynomial regression. Sampling properties of the proposed estimation procedure are studied. We derive the asymptotic bias, variance and normality of the proposed estimate. Asymptotic relative efficiency of the proposed estimate with respect to the local polynomial regression is investigated. It is shown that the proposed estimate can be much more efficient than the local polynomial regression estimate for various non-normal errors, while being almost as efficient as the local polynomial regression estimate for normal errors. Simulation is conducted to examine the performance of the proposed estimates. The simulation results are consistent with our theoretic findings. A real data example is used to illustrate the proposed method.
