We propose a multithreshold change plane regression model which naturally partitions the observed subjects into subgroups with different covariate effects. The underlying grouping variable is a linear function of observed covariates and thus multiple thresholds produce change planes in the covariate space. We contribute a novel two-stage estimation approach to determine the number of subgroups, the location of thresholds, and all other regression parameters. In the first stage we adopt a group selection principle to consistently identify the number of subgroups, while in the second stage change point locations and model parameter estimates are refined by a penalized induced smoothing technique. Our procedure allows sparse solutions for relatively moderate- or high-dimensional covariates. We further establish the asymptotic properties of our proposed estimators under appropriate technical conditions. We evaluate the performance of the proposed methods by simulation studies and provide illustrations using two medical data examples. Our proposal for subgroup identification may lead to an immediate application in personalized medicine.

中文翻译：

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多阈值变化平面模型：估计理论及其在子群识别中的应用

我们提出了一个多阈值变化平面回归模型，该模型自然地将观察到的受试者划分为具有不同协变量效应的子组。基础分组变量是观察到的协变量的线性函数，因此多个阈值会在协变量空间中产生变化平面。我们提供了一种新颖的两阶段估计方法来确定子组的数量、阈值的位置和所有其他回归参数。在第一阶段，我们采用组选择原则来一致地识别子组的数量，而在第二阶段，变化点位置和模型参数估计通过惩罚诱导平滑技术进行细化。我们的过程允许相对中等或高维协变量的稀疏解决方案。我们在适当的技术条件下进一步建立了我们提出的估计量的渐近性质。我们通过模拟研究评估所提出方法的性能，并使用两个医学数据示例提供说明。我们对亚组识别的提议可能会立即应用于个性化医疗。