误差分布未知下时空模型的自适应非参数估计

Adaptive Nonparametric Estimation of Spatio-Temporal Models with Unknown Error Distributions

极大似然估计作为参数估计中较为有效的一种估计方法,在误差分布未知下无法进行,另一方面,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.考虑时空异质性和相关性,针对误差分布未知的时空模型,本文提出基于核密度估计的自适应非参数估计方法.在较弱的条件下证明了该估计量和已知误差分布下的局部极大似然估计量是渐近等效,比基于最小二乘的局部多项式估计量有效.模拟和实证都验证了该方法对于有限样本的有效性,尤其奇异点的存在,该方法在边界的拟合效果显著优于基于最小二乘的方法.

Maximum likelihood is an effective method for parameter estimation,but it canJt work with unknown error distribution.On the other hand,when the data contain outliers or come from population with heavy-tailed distributions,which appear very often in spatiotemporal data,the estimation methods based on least-squares method will not perform well.Considering the spatio-temporal heterogeneity and correlation,in this paper,the authors propose an adaptive nonparametric estimator for spatio-temporal model with unknown error distributions based on kernel density estimation.Asymptotic theory properties show that the proposed estimator is as asymptotically efficient as local maximum likelihood estimator with known error distributions,and more efficient than,local polynomial estimator based on least-square method under some mild conditions.Simulation and case study are conducted to investigate the finite-sample performance of our procedure,especially for the existence of singularities,for boundary points,the performance of our procedure is significantly better than the method based on least squares.