部分线性空间自回归模型的惩罚最小二乘方法

Penalized Least Squares Method of Partially Linear Spatial Autoregressive Model

部分线性空间自回归模型因具有参数空间自回归模型的解释能力和非参数空间自回归模型的灵活性而成为一类备受关注的半参数空间自回归模型。主要研究部分线性空间自回归模型的变量选择问题,基于轮廓拟最大似然方法和一类非凸罚函数,提出了一类惩罚最小二乘方法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回归系数。在适当的正则条件下,推导了回归系数的惩罚估计的收敛速度,并证明了所提出的变量选择方法具有Oracle性质。模拟研究和实际数据分析均表明所提出的变量选择方法具有满意的有限样本性质。

Partially linear spatial autoregressive model has attracted extensive attention in recent years because it combines explanatory power of parametric spatial autoregressive models and flexibility of nonparametric spatial autoregressive model.This paper considers the problem of variable selection in the partially linear spatial autoregressive model.Based on profile quasimaximum likelihood method and a class of non-convex penalty function,a class of penalized least squares method is proposed to simultaneously select significant explanatory variables in parametric component of the model and estimate corresponding nonzero regression coefficients.Under appropriate regularity conditions,the rate of convergence of the penalized estimator of the regression coefficient vector is derived and it shows that the proposed variable selection method enjoys oracle property.Both simulation studies and real data analysis indicate that the proposed variable selection method has satisfactory finite sample performance.