Variable selection has played a fundamental role in regression analysis. Spatial autoregressive model is a useful tool in econometrics and statistics in which context variable selection is necessary but not adequately investigated. In this paper, we consider conducting variable selection in spatial autoregressive models with a diverging number of parameters. Smoothly clipped absolute deviation penalty is considered to obtain the estimators. Moreover the dimension of the covariates are allowed to vary with sample size. In order to attenuate the bias caused by endogeneity, instrumental variable is adopted in the estimation procedure. The proposed method can do parametric estimation and variable selection simultaneously. Under mild conditions, we establish the asymptotic and oracle property of the proposed estimators. Finally, the performance of the proposed estimation procedure is examined via Monte Carlo simulation studies and a data set from a Boston housing price is analyzed as an illustrative example.

中文翻译：

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具有不同数量参数的空间自回归模型的变量选择

变量选择在回归分析中发挥了基本作用。空间自回归模型在计量经济学和统计学中是一个有用的工具，其中上下文变量的选择是必要的，但没有得到充分的研究。在本文中，我们考虑在具有不同参数数量的空间自回归模型中进行变量选择。平滑剪裁的绝对偏差惩罚被认为是获得估计量。此外，协变量的维度可以随样本大小而变化。为了减弱内生性引起的偏差，估计过程中采用了工具变量。该方法可以同时进行参数估计和变量选择。在温和的条件下，我们建立了所提出的估计量的渐近和预言性质。最后，