The assumption of equal variances is not always appropriate and different approaches for modelling variance heterogeneity have been widely studied in the literature. One of these approaches is joint location and scale model defined with the idea that both the location and the scale depend on explanatory variables through parametric linear models. Because the joint location and scale model includes two models, it does not deal well with a large number of irrelevant variables. Therefore, determining the variables that are important for the location and the scale is as important as estimating the parameters of these models. From this point of view, a combine robust estimation and variable selection method is proposed to simultaneously estimate the parameters and select the important variables. This is done using the least favorable distribution and least absolute shrinkage and selection operator method. Under appropriate conditions, we study the consistency, asymptotic distribution and the sparsity property of the proposed robust estimator. Simulation studies and a real data example are provided to demonstrate the advantages of the proposed method over existing methods in literature.

方差相等的假设并不总是合适的，并且在文献中已经广泛研究了用于建模方差异质性的不同方法。这些方法之一是联合位置和比例模型，其定义是位置和比例都取决于参数线性模型中的解释变量。因为联合位置和比例模型包括两个模型，所以它不能很好地处理大量不相关的变量。因此，确定对位置和比例重要的变量与估算这些模型的参数一样重要。从这一观点出发，提出了一种鲁棒估计和变量选择相结合的方法，以同时估计参数和选择重要变量。这是使用最不利的分布和最小绝对收缩和选择算子方法完成的。在适当的条件下，我们研究了所提出的鲁棒估计量的一致性，渐近分布和稀疏性。仿真研究和实际数据示例提供了证明该方法相对于文献中现有方法的优势。