空间回归模型估计中的最小二乘法

空间回归模型由于引入了空间地理信息而使得其参数估计变得复杂,因为主要采用最大似然法,致使一般人认为在空间回归模型参数估计中不存在最小二乘法。通过分析空间回归模型的参数估计技术,研究发现,最小二乘法和最大似然法分别用于估计空间回归模型的不同的参数,只有将两者结合起来才能快速有效地完成全部的参数估计。数理论证结果表明,空间回归模型参数最小二乘估计量是最佳线性无偏估计量。空间回归模型的回归参数可以在估计量为正态性的条件下而实施显著性检验,而空间效应参数则不可以用此方法进行检验。

The Least Squares of Spatial Regression Models

Due to the introduction of the geospatial information, the parameter estimation of the spatial regression models becomes complexity, it is estimated by maximum likelihood method. Most people consider spatial regression parameter estimation of least squares do not exist in the model. This paper makes a research about least squares estimate method of spatial regression models. The study found that least squares and maximum likelihood method for different parameters estimation of spatial regression models, and combination of the two methods can quickly and efficiently complete the full parameter estimation. The mathematical analysis results indicate that spatial regression model parameters of least squares estimator is the best linear unbiased estimator, and the regression parameters can be made significant tests under normality distribution, but spatial effect parameter is not available.