空间变系数模型的二元惩罚样条分位回归估计

Estimation of Bivariate Penalty Spline Quantile Regression for Spatial Varying Coefficient Models

空间变系数模型是一种研究空间非平稳数据的有效工具。本文介绍了空间变系数非参数回归模型,研发了的一种基于二元惩罚样条逼近的分位回归估计方法,该估计方法不仅可以处理具有复杂边界、不规则形状的空间区域,而且还展现出不同分位水平下的解释能力。在两种不同的情形下,分别给出了所提出估计量的理论性质,即收敛速率和渐近分布。对于参数的估计过程,提出一种基于交替方向乘子(ADMM)迭代算法实现模型的求解。数值模拟结果显示本文提出的估计方法比均值意义下更稳健。最后,利用我国空气质量实际数据说明该模型及估计方法的应用价值。

Spatial varying coefficient model is an effective tool to study spatial nonstationary data.In this paper,a quantile regression estimation method based on bivariate penalty spline approximation for nonparametric regression models with spatial varying coeficients is proposed.This estimation method can not only deal with the spatial regions with complex boundaries and irregular shapes,but also show the ability of interpretation at different quantile levels.In two different cases,the theoretical properties of the proposed estimator,namely the rate of convergence and asymptotic distribution,are given respectively.For the estimation process,we use ADMM iterative algorithm to solve the model.For the goodness of fit of the model,we propose a coefficient robustness test method based on Boostrap method,and gives the test implementation algorithm.Numerical simulation results show that the proposed estimation method is more robust than the sense of mean regression.Finally,the application value of the model and the estimation method is illustrated by the actual data of Air Quality in China.