Spatial autoregressive model is widely concerned in the economic field, whereas when the data is missing, variable selection and parameter estimation of the model is quite challenging. Based on this, we discuss the variable selection in spatial autoregressive model with missing data. Under the condition that errors are independent and identically distributed, we have developed a penalized quasi-maximum likelihood method to achieve variable selection and parameter estimation simultaneously in the presence of missing responses. The method’s theoretical properties, including consistency and asymptotical normality, are established under certain assumptions. Meanwhile, an improved expectation–maximization algorithm is provided for optimizing the penalized quasi-maximum likelihood function. Simulations are conducted to examine the proposed method and assess the finite-sample performance. Additionally, we present a practical example to illustrate the method’s application.

空间自回归模型在经济领域受到广泛关注，但当数据缺失时，模型的变量选择和参数估计相当具有挑战性。在此基础上，我们讨论了缺失数据的空间自回归模型中的变量选择。在误差独立同分布的条件下，我们开发了一种惩罚准极大似然方法，在存在缺失响应的情况下同时实现变量选择和参数估计。该方法的理论特性，包括一致性和渐近正态性，是在某些假设下建立的。同时，提出了一种改进的期望最大化算法来优化惩罚准最大似然函数。进行模拟来检查所提出的方法并评估有限样本性能。此外，我们还提供了一个实际示例来说明该方法的应用。