In this paper, we explore sparsity and homogeneity of regression coefficients incorporating prior constraint information. The sparsity means that a small fraction of regression coefficients is nonzero, and the homogeneity means that regression coefficients are grouped and have exactly the same value in each group. A general pairwise fusion approach is proposed to deal with the sparsity and homogeneity detection when combining prior convex constraints. We develop a modified alternating direction method of multipliers algorithm to obtain the estimators and demonstrate its convergence. The efficiency of both sparsity and homogeneity detection can be improved by combining the prior information. Our proposed method is further illustrated by simulation studies and analysis of an ozone dataset.

中文翻译：

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结合先验约束信息的成对融合方法

在本文中，我们探索了结合先验约束信息的回归系数的稀疏性和同质性。稀疏性意味着一小部分回归系数不为零，同质性意味着对回归系数进行了分组并在每组中具有完全相同的值。提出了一种通用的成对融合方法来处理在组合先前凸约束时的稀疏性和同质性检测。我们开发了一种改进的乘数交替方向算法，以获得估计量并证明其收敛性。通过组合先验信息可以提高稀疏性和同质性检测的效率。通过对臭氧数据集的仿真研究和分析，可以进一步说明我们提出的方法。