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Consistent Model Selection in Segmented Line Regression.

Jeankyung Kim1, Hyune-Ju Kim2

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Summary
This summary is machine-generated.

This study introduces a modified Schwarz criterion (Bayes Information Criterion) to accurately detect change-points in segmented line regression. The modified criterion demonstrates consistency in identifying the correct number of change-points, improving upon traditional methods.

Keywords:
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Area of Science:

  • Statistics
  • Regression Analysis
  • Change-Point Detection

Background:

  • The Bayes Information Criterion (BIC) is commonly used for model selection.
  • Traditional BIC may overestimate change-points in segmented regression.
  • Existing modified BIC versions have limitations in change-point problems.

Purpose of the Study:

  • To develop and analyze a modified Schwarz criterion for selecting the number of change-points in segmented line regression.
  • To address the overestimation tendency of traditional BIC in change-point detection.
  • To investigate the asymptotic properties of the proposed criterion.

Main Methods:

  • Considered a segmented line regression model with an unknown number of change-points.
  • Proposed a modified Schwarz type criterion with a harsher penalty.
  • Proved the consistency of the modified criterion for models without continuity constraints.
  • Conducted simulations to support theoretical findings and compare with existing methods.

Main Results:

  • The modified Schwarz criterion consistently selects the correct number of change-points in segmented line regression without continuity constraints.
  • Simulation results support the theoretical consistency of the proposed method.
  • For models with continuity constraints, the modified BIC shows comparable asymptotic behavior to the Liu, Wu, and Zidek (1997) criterion.

Conclusions:

  • The proposed modified Schwarz criterion offers a consistent approach for change-point detection in segmented line regression.
  • This modification effectively mitigates the overestimation issue associated with traditional BIC.
  • The criterion shows promise for both constrained and unconstrained segmented regression models.