空间部分线性变系数模型的分位回归估计

Quantile Regression Estimation of Spatial Partial Linear Variable Coefficient Models

文章针对空间数据统计与回归建模,提出空间部分线性变系数模型,并提出了一种基于二元惩罚样条的非参数逼近分位回归估计方法。该方法不仅可以有效地处理变系数部分复杂边界、不规则形状的空间区域划分和非参数函数的逼近,而且整体上展现出不同分位水平下的解释能力。同时,针对模型实现问题,还提出了基于交替方向乘子法(ADMM)的参数估计算法,数值模拟说明该方法的估计结果更加稳健、有效。

Aiming at spatial data statistics and regression modeling,this paper proposes spatial partial linear variable coefficient models,and then puts forward a nonparametric approximation quantile regression estimation method based on binary penalty spline.This method can not only effectively deal with the complex boundary of variable coefficient,the division of space in ir-regular shape and the approximation of nonparametric function,but also show the ability of interpretation at different quantile levels.At the same time,the paper presents a parameter estimation algorithm based on alternating direction multiplier method(ADMM)to solve the problem of model implementation.Numerical simulation shows that the estimation result of this method is more robust and effective.