Consistent model selection in segmented line regression

Jeankyung Kim, Heather Hyune-Ju Kim

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

The Schwarz criterion or Bayes Information Criterion (BIC) is often used to select a model dimension, and some variations of the BIC have been proposed in the context of change-point problems. In this paper, we consider a segmented line regression model with an unknown number of change-points and study asymptotic properties of Schwarz type criteria in selecting the number of change-points. Noticing the over-estimating tendency of the traditional BIC observed in some empirical studies and being motivated by asymptotic behavior of the modified BIC proposed by Zhang and Siegmund (2007), we consider a variation of the Schwarz type criterion that applies a harsher penalty equivalent to the model with one additional unknown parameter per segment. For the segmented line regression model without the continuity constraint, we prove the consistency of the number of change-points selected by the criterion with such type of a modification and summarize the simulation results that support the consistency. Further simulations are conducted for the model with the continuity constraint, and we empirically observe that the asymptotic behavior of this modified version of BIC is comparable to that of the criterion proposed by Liu et al. (1997).

Original languageEnglish (US)
Pages (from-to)106-116
Number of pages11
JournalJournal of Statistical Planning and Inference
Volume170
DOIs
StatePublished - 2016

Keywords

  • Bayes information criterion
  • Model selection
  • Segmented line regression

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Applied Mathematics
  • Statistics and Probability

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