Efficient estimation and inferences for varying-coefficient models
Efficient estimation and inferences for varying-coefficient models
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DOI：
10.2307/2669472
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发表时间：
2000-09-01
影响因子：
3.7
通讯作者：
Li, RZ
中科院分区：
文献类型：
--
作者：
Cai, ZW;Fan, JQ;Li, RZ
本文基于哈斯蒂（Hastie）和蒂布希拉尼（Tibshirani）提出的变系数模型进行统计推断。使用局部多项式回归技术来估计系数函数，并建立了所得估计量的渐近正态性。推导了估计系数的标准误差公式，并进行了实证检验。还提出了一种基于非参数极大似然比类型检验的拟合优度检验技术，用于检测变系数模型中的某些系数函数是否为常数，或者模型中的任何协变量是否在统计上显著。通过条件自助法估计检验的零分布。我们的估计技术涉及求解数百个局部似然方程。为了减轻计算负担，提出并实施了一步牛顿 - 拉夫森（Newton - Raphson）估计量。结果表明，所得的一步法在渐近和实证上都能在性能不下降的情况下节省数十倍的计算成本。通过模拟数据和实际数据的例子来说明我们提出的方法。
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 far 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.