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- Title
Determining the number of change-point via high-dimensional cross-validation.
- Authors
Haiyan Jiang; Jiaqi Li; Zhonghua Li
- Abstract
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.
- Subjects
CHANGE-point problems; ERROR functions; FORECASTING; DYNAMIC programming
- Publication
Stat, 2020, Vol 9, Issue 1, p1
- ISSN
2049-1573
- Publication type
Article
- DOI
10.1002/sta4.284