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Determining the number of change‐point via high‐dimensional cross‐validation
Author(s) -
Jiang Haiyan,
Li Jiaqi,
Li Zhonghua
Publication year - 2020
Publication title -
stat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.61
H-Index - 18
ISSN - 2049-1573
DOI - 10.1002/sta4.284
Subject(s) - curse of dimensionality , dimension (graph theory) , model selection , information criteria , quadratic equation , mathematics , selection (genetic algorithm) , function (biology) , cross validation , point (geometry) , sample size determination , high dimensional , measure (data warehouse) , computer science , mathematical optimization , statistics , data mining , artificial intelligence , geometry , evolutionary biology , pure mathematics , biology
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.