In multiple change‐point analysis, one of the major challenges is the determination of the number of change points, which is usually cast as a model selection problem. However, for model selection methods based on the Schwarz information criterion (SIC), it is typical that different penalization terms are required for different change‐point problems and the optimal penalization magnitude usually varies with the model and error distributions. In order to estimate the number of change points in high dimension, we develop a high‐dimensional data‐driven cross‐validation selection criterion. First, we define a goodness‐of‐fit measure by incorporating the dimensionality into the quadratic prediction error function. Second, the high‐dimensional cross‐validation (hCV) procedure is applied based on an order‐preserved sample‐splitting strategy. Simulation studies show that the proposed hCV criterion has more robust performance compared with a high‐dimensional SIC criterion tailored for the high‐dimensional change‐point problem. The selection property is also established under some mild conditions.

中文翻译：

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通过高维交叉验证确定变更点的数量

在多变更点分析中，主要挑战之一是确定变更点数，通常将其确定为模型选择问题。但是，对于基于Schwarz信息标准（SIC）的模型选择方法，通常对于不同的变更点问题需要使用不同的惩罚项，并且最佳惩罚幅度通常会随模型和误差分布而变化。为了估计高维中的变更点数，我们开发了一个高维数据驱动的交叉验证选择准则。首先，我们通过将维数纳入二次预测误差函数来定义拟合优度度量。其次，基于保留订单的样本拆分策略应用高维交叉验证（hCV）程序。仿真研究表明，与针对高维变化点问题量身定制的高维SIC标准相比，拟议的hCV标准具有更强的性能。在某些温和条件下也可以建立选择属性。