The partially linear varying coefficient spatial autoregressive model is a recently proposed semi-parametric spatial autoregressive model, in which some of the explanatory variables have varying coefficients while the remained explanatory variables possess constant ones. Although some estimation methods have been proposed for the partially linear varying coefficient spatial autoregressive model, the problem of selecting important explanatory variables in the parametric component of such model has not been addressed to date. In this paper, we propose a penalized profile least squares method to address this problem. Different from the existing estimation methods, the proposed method can simultaneously select the significant explanatory variables in the parametric component and estimate the corresponding nonzero regression coefficients. Furthermore, we provide a computationally feasible algorithm to obtain the penalized profile least squares estimator. The finite sample performance of the proposed variable selection method is evaluated through some simulation studies and illustrated by a real data example.

中文翻译：

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部分线性变系数空间自回归模型的变量选择

部分线性变系数空间自回归模型是最近提出的半参数空间自回归模型，其中一些解释变量具有可变系数，而其余解释变量具有恒定系数。尽管针对部分线性变系数空间自回归模型提出了一些估计方法，但迄今为止尚未解决在此类模型的参数分量中选择重要解释变量的问题。在本文中，我们提出了一种惩罚轮廓最小二乘法来解决这个问题。与现有的估计方法不同，该方法可以同时选择参数分量中显着的解释变量，并估计相应的非零回归系数。此外，我们提供了一种计算上可行的算法来获得惩罚的轮廓最小二乘估计量。通过一些模拟研究评估了所提出的变量选择方法的有限样本性能，并通过实际数据示例进行了说明。