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Statistica Sinica 19 (2009), 597-609





SELECTING THE NUMBER OF CHANGE-POINTS

IN SEGMENTED LINE REGRESSION


Hyune-Ju Kim, Binbing Yu and Eric J. Feuer


Syracuse University, National Institute of Aging,
and National Cancer Institute


Abstract: Segmented line regression has been used in many applications, and the problem of estimating the number of change-points in segmented line regression has been discussed in Kim et al. (2000). This paper studies asymptotic properties of the number of change-points selected by the permutation procedure of Kim et al. (2000). This procedure is based on a sequential application of likelihood ratio type tests, and controls the over-fitting probability by its design. In this paper we show that, under some conditions, the number of change-points selected by the permutation procedure is consistent. Via simulations, the permutation procedure is compared with such information-based criterior as the Bayesian Information Criterion (BIC), the Akaike Information Criterion (AIC), and Generalized Cross Validation (GCV).



Key words and phrases: Change-points, model selection, permutation test, segmented line regression.
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