In many problems, one has several models of interest that capture key parameters describing the distribution of the data. Partially overlapping models are taken as models in which at least one covariate effect is common to the models. A priori knowledge of such structure enables efficient estimation of all model parameters. However, in practice, this structure may be unknown. We propose adaptive composite M-estimation (ACME) for partially overlapping models using a composite loss function, which is a linear combination of loss functions defining the individual models. Penalization is applied to pairwise differences of parameters across models, resulting in data driven identification of the overlap structure. Further penalization is imposed on the individual parameters, enabling sparse estimation in the regression setting. The recovery of the overlap structure enables more efficient parameter estimation. An oracle result is established. Simulation studies illustrate the advantages of ACME over existing methods that fit individual models separately or make strong a priori assumption about the overlap structure.

中文翻译：

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具有部分重叠模型的自适应估计

在许多问题中，有几个感兴趣的模型可以捕获描述数据分布的关键参数。部分重叠模型被视为模型中至少有一个协变量效应是模型共有的。这种结构的先验知识能够有效地估计所有模型参数。然而，在实践中，这种结构可能是未知的。我们为使用复合损失函数的部分重叠模型提出了自适应复合 M 估计 (ACME)，复合损失函数是定义单个模型的损失函数的线性组合。惩罚应用于模型间参数的成对差异，导致数据驱动的重叠结构识别。对各个参数施加进一步的惩罚，从而在回归设置中进行稀疏估计。重叠结构的恢复可以实现更有效的参数估计。一个oracle结果成立。模拟研究说明了 ACME 优于现有方法的优势，现有方法分别拟合单个模型或对重叠结构做出强烈的先验假设。