时空模型的局部众数回归

Local modal regression for the spatio-temporal model

时空数据经常含有奇异点或来自重尾分布,此时基于最小二乘的估计方法效果欠佳,需要更稳健的估计方法.本文提出时空模型的基于局部众数(local modal, LM)的局部线性估计方法.理论和数据分析结果都显示,若数据含有奇异点或来自重尾分布,基于局部众数的局部线性方法比基于最小二乘的局部线性方法有效;若数据无奇异点且来自正态分布,两种方法效率渐近一致.本文采用众数期望最大化(modal expectation-maximization, MEM)算法,并在数据相依情形下得出估计量的渐近正态性.

When the data contain outliers or come from population with heavy-tailed distributions, which appear very often in spatio-temporal data, the estimation methods based on the least square method will not perform well. More robust estimation methods are required. We propose the local linear estimation for the spatio-temporal model based on the local modal method. Asymptotic theory properties and data analysis results show that the proposed estimator is more efficient than the ordinary least square-based estimation in the case of outliers or heavy-tailed error distributions, and as asymptotically efficient as the least square estimator when there are no outliers and the error is a normal distribution. The modal expectation-maximization algorithm is adopted and the asymptotic distributions of estimators are driven when the data are mixing correlation.