This paper studies a partially linear additive regression with spatial data. A new estimation procedure is developed for estimating the unknown parameters and additive components in regression. The proposed method is suitable for high dimensional data, there is no need to solve the restricted minimization problem and no iterative algorithms are needed. Under mild regularity assumptions, the asymptotic distribution of the estimator of the unknown parameter vector is established, the asymptotic distributions of the estimators of the unknown functions are also derived. Finite sample properties of our procedures are studied through Monte Carlo simulations. A real data example about spatial soil data is used to illustrate our proposed methodology.

本文研究了空间数据的部分线性加性回归。开发了一种新的估计程序，用于估计回归中的未知参数和附加分量。该方法适用于高维数据，无需解决受限最小化问题，也无需迭代算法。在温和的正则假设下，建立了未知参数向量估计量的渐近分布，并推导出了未知函数估计量的渐近分布。通过蒙特卡罗模拟研究了我们程序的有限样本属性。一个关于空间土壤数据的真实数据示例用于说明我们提出的方法。