部分线性变系数空间自回归模型的惩罚轮廓拟最大似然方法

Penalized Profile Quasi-maximum Likelihood Method of Partially Linear Varying Coefficient Spatial Autoregressive Model

主要研究了部分线性变系数空间自回归模型的变量选择问题。结合拟最大似然方法、局部线性光滑方法以及一类非凸罚函数,提出了一个变量选择方法用于同时选择该模型的参数部分中重要解释变量和估计相应的非零参数。大量模拟研究表明,所提出的变量选择方法具有满意的有限样本性质,并且关于空间权矩阵的稀疏度、空间相关强度、系数函数的复杂度以及误差分布的非正态性非常稳健。特别地,当样本容量较大且罚函数选择合适时,即使解释变量的相关性较强或者模型中含有较多不重要解释变量,所提出的变量选择方法仍然具有比较满意的有限样本性质。通过分析波士顿房屋价格数据考察了所提出的变量选择方法的实际应用效果。

The problem of variable selection is considered in partially linear varying coefficient spatial autoregressive model.By combining profile quasi-maximum likelihood method and a class of non-convex penalty function,a variable selection method is proposed to simultaneously select important explanatory variables in parametric component of the partially linear varying coefficient spatial autoregressive model and estimate the corresponding nonzero parameters.Extensive simulation studies show that the proposed variable selection method is of satisfactory finite sample performance.Especially,the proposed variable selection method is quite robust to degree of sparseness of spatial weight matrix,intensity of spatial dependence,degree of complexity of coefficient function and non-normality of error distribution,and even works well in the case where correlation among explanatory variables is strong or number of unimportant explanatory variables is large provided that appropriate penalty function is used and sample size is moderately large.As an illustrative example,the proposed variable selection method is applied to analyze the popular Boston housing price data.