CONSISTENT SELECTION OF THE NUMBER OF CHANGE-POINTS VIA SAMPLE-SPLITTING.
CONSISTENT SELECTION OF THE NUMBER OF CHANGE-POINTS VIA SAMPLE-SPLITTING.
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DOI：
10.1214/19-aos1814
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发表时间：
2020-02
影响因子：
4.5
通讯作者：
Changliang Zou;Guanghui Wang;Runze Li
中科院分区：
文献类型：
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作者：
Changliang Zou;Guanghui Wang;Runze Li
在多个变点分析中，主要的挑战之一是估计变点的数量。大多数现有的方法试图最小化的施瓦茨信息标准，平衡一个长期量化模型拟合与惩罚长期会计模型的复杂性，增加了变点的数量和限制过拟合。然而，不同的惩罚条款，以适应不同的情况下，多个变点问题和最佳的惩罚幅度通常不同的模型和误差分布。我们提出了一个数据驱动的选择标准，适用于大多数流行的变点检测方法，包括二进制分割和最佳分割算法。关键思想是选择使预测误差平方最小的变点数量，预测误差平方衡量的是指定模型对新样本的拟合程度。基于保序样本分裂策略，提出了一种交叉验证估计方案，并在较弱的条件下证明了其渐近选择相合性。所提出的选择标准的有效性证明了各种数值实验和实际数据的例子。
In multiple change-point analysis, one of the major challenges is to estimate the number of change-points. Most existing approaches attempt to minimize a Schwarz information criterion which balances a term quantifying model fit with a penalization term accounting for model complexity that increases with the number of change-points and limits overfitting. However, different penalization terms are required to adapt to different contexts of multiple change-point problems and the optimal penalization magnitude usually varies from the model and error distribution. We propose a data-driven selection criterion that is applicable to most kinds of popular change-point detection methods, including binary segmentation and optimal partitioning algorithms. The key idea is to select the number of change-points that minimizes the squared prediction error, which measures the fit of a specified model for a new sample. We develop a cross-validation estimation scheme based on an order-preserved sample-splitting strategy, and establish its asymptotic selection consistency under some mild conditions. Effectiveness of the proposed selection criterion is demonstrated on a variety of numerical experiments and real-data examples.