ROBUST LOCAL POLYNOMIAL REGRESSION FOR DEPENDENT DATA
ROBUST LOCAL POLYNOMIAL REGRESSION FOR DEPENDENT DATA
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发表时间：
2001
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通讯作者：
Jiancheng Jiang;Y. P. Mack
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作者：
Jiancheng Jiang;Y. P. Mack
设（Xj，Yj）n=1是二元联合严格平稳过程的一个实现.本文考虑回归函数m（x）= E（Y）的一个稳健估计|X = x）的局部多项式回归方法。该估计量是一个局部M-估计量加权的核函数。在许多时间序列模型所满足的混合条件下，结合其他适当的条件，建立了相容性和渐近正态性结果。引入一步局部M-估计以减少计算负担。此外，我们给出了一个数据驱动的选择最小化的比例因子，涉及的渐近协方差表达式中的函数，通过绘制一个平行的胡贝尔的函数类。该方法通过两个例子来说明。
Let (Xj ,Y j) n=1 be a realization of a bivariate jointly strictly station- ary process. We consider a robust estimator of the regression function m(x )= E(Y |X = x) by using local polynomial regression techniques. The estimator is a local M-estimator weighted by a kernel function. Under mixing conditions satisfied by many time series models, together with other appropriate conditions, consistency and asymptotic normality results are established. One-step local M-estimators are introduced to reduce computational burden. In addition, we give a data-driven choice for minimizing the scale factor involving the ψ-function in the asymptotic covariance expression, by drawing a parallel with the class of Huber's ψ-functions. The method is illustrated via two examples.