Regression analysis is commonly conducted in survey sampling. However, existing methods fail when the relationships vary across different areas or domains. In this paper, we propose a unified framework to study the group-wise covariate effect under complex survey sampling based on pairwise penalties, and the associated objective function is solved by the alternating direction method of multipliers. Theoretical properties of the proposed method are investigated under some generality conditions. Numerical experiments demonstrate the superiority of the proposed method in terms of identifying groups and estimation efficiency for both linear regression models and logistic regression models.

翻译：回归分析在调查抽样中广泛应用。然而，当不同区域或领域存在关系变化时，现有方法会失效。本文提出一个统一框架，基于成对惩罚项研究复杂调查抽样下的分组协变量效应，并通过交替方向乘子法求解相应的目标函数。在一般性条件下，我们探讨了该方法的理论性质。数值实验表明，对于线性回归模型和逻辑回归模型，该方法在分组识别和估计效率方面均具有优越性。