ASYMPTOTIC THEORY FOR ZERO ENERGY FUNCTIONALS WITH NONPARAMETRIC REGRESSION APPLICATIONS
给出了非平稳时间序列中零能量函数样本均值的局部极限定理，该结果适用于非参数核密度估计和回归问题，并发现非参数回归中线性项从渐近偏差中消除，使Nadaraya-Watson估计量与局部线性估计量具有相同的极限分布。
A local limit theorem is given for the sample mean of a zero energy function of a nonstationary time series involving twin numerical sequences that pass to infinity. The result is applicable in certain nonparametric kernel density estimation and regression problems where the relevant quantities are functions of both sample size and bandwidth. An interesting outcome of the theory in nonparametric regression is that the linear term is eliminated from the asymptotic bias. In consequence and in contrast to the stationary case, the Nadaraya–Watson estimator has the same limit distribution (to the second order including bias) as the local linear nonparametric estimator.