基于Monte Carlo模拟比较K近邻和局部线性分位数回归

局部线性分位数回归是目前比较流行的非参数分位数回归,其潜在假定待估函数线性光滑.K近邻分位数回归也是非参数分位数回归的重要组成部分,其具有不需待估函数光滑和不同分位点的回归曲线不相交等优点.通过Monte Carlo模拟,比较了两者的估计,得到当待估函数的跳跃点或突变点比较多时,K近邻分位数回归的拟合效果优于局部线性回归.其中模拟的函数是Blocks、Bumps和HeaviSine的函数,它们分别代表跳跃性、波动性、斜率突变性的函数.

A Comparison of K Nearest Neighbor Quantile Regression and Local Linear Quantile Regression Based on Monte Carlo Simulation

Local linear quantile regression is a popular method of nonparametric quantile regression,which assumes smoothness of functions.K nearest neighbor regression is also a key important part of nonparametric quantile regression,which has many advantages,such as not assuming smoothness of functions,noncrossing of regression curves of different quantile and so on.The paper carries out Monte Carlo simulations to compare the two models.When function to be estimated has some jump points or catastrophe points,K nearest-neighbor quantile regression is superior to local linear quantile regression.In addition,simulated function is Blocks,Bumps and HeaviSine,which stand for jumping,volatility,mutagenicity slope function.