Efficient Estimation and Inferences for Varying-Coefficient Models
本文用局部多项式回归估计变系数模型的系数函数，推导了估计量的渐近正态性和标准误公式，并提出了基于非参数似然比检验的拟合优度检验方法，同时用一步牛顿-拉夫森估计大幅降低计算成本。
Abstract This article deals with statistical inferences based on the varying-coefficient models proposed by Hastie and Tibshirani. Local polynomial regression techniques are used to estimate coefficient functions, and the asymptotic normality of the resulting estimators is established. The standard error formulas for estimated coefficients are derived and are empirically tested. A goodness-of-fit test technique, based on a nonparametric maximum likelihood ratio type of test, is also proposed to detect whether certain coefficient functions in a varying-coefficient model are constant or whether any covariates are statistically significant in the model. The null distribution of the test is estimated by a conditional bootstrap method. Our estimation techniques involve solving hundreds of local likelihood equations. To reduce the computational burden, a one-step Newton-Raphson estimator is proposed and implemented. The resulting one-step procedure is shown to save computational cost on an order of tens with no deterioration in performance, both asymptotically and empirically. Both simulated and real data examples are used to illustrate our proposed methodology.