变系数模型的局部加权组合分位数估计  

Local Weighted Composite Quantile Estimating for Varying Coefficient Models

作　　者：解其昌[1] 吕秀梅[2] 

机构地区：[1]山东工商学院经济学院,烟台264005 [2]重庆工商大学财政金融学院,重庆400067

出　　处：《应用概率统计》2014年第6期631-650,共20页Chinese Journal of Applied Probability and Statistics

基　　金：教育部基金(109140);山东工商学院博士启动基金(521014306203)资助

摘　　要：变系数模型是经典线性模型的推广,它以更加灵活的形式来模拟变量间的非线性关系.采用局部加权组合分位数方法来估计模型的系数函数.推导出估计量的局部Bahadur表示以及渐近正态性.构造一个二次规划,给出了最优权重的选择方法.对于非正态误差分布,理论分析和数值模拟表明局部加权组合分位数比局部最小二乘估计有更高的效率;而对于正态误差分布,局部加权组合分位数与局部最小二乘估计有着几乎同样的效率.通过Monte Carlo模拟和实证分析,检验估计量的有限样本性质,结果与理论相一致.A generalization of classical linear models is varying coefficient models, which offer a flexible approach to modeling nonlinearity between covariates. A method of local weighted composite quantile regression is suggested to estimate the coefficient functions. The local Bahadur representation of the local estimator is derived and the asymptotic normality of the resulting estimator is established. Comparing to the local least squares estimator, the asymptotic relative efficiency is examined for the local weighted composite quantile estimator. Both theoretical analysis and numerical simulations reveal that the local weighted composite quantile estimator can obtain more efficient than the 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 least squares estimator. Monte Carlo results are consistent with our theoretical findings. An empirical application demonstrates the potential of the proposed method.

关 键 词：变系数模型 渐近正态性 渐近相对效率 局部加权组合分位数估计 

分 类 号：O212.2[理学—概率论与数理统计]