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Robust bent line regression.

Feipeng Zhang1,2, Qunhua Li1

  • 1Department of Statistics, Pennsylvania State University, PA, 16802, USA.

Journal of Statistical Planning and Inference
|September 26, 2017
PubMed
Summary
This summary is machine-generated.

We developed a new rank-based method for detecting change points in linear regression. This robust approach efficiently estimates parameters and tests for changes, even with outliers.

Keywords:
Bent line regressionChange pointRank-based regressionRobust estimationWeighted CUSUM test

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Area of Science:

  • Statistics
  • Econometrics
  • Data Science

Background:

  • Change point detection is crucial for analyzing time series data and identifying structural breaks.
  • Traditional methods can be sensitive to outliers and computationally intensive.

Purpose of the Study:

  • To introduce a novel rank-based bent linear regression method for detecting unknown change points.
  • To develop a computationally efficient estimation and hypothesis testing framework for change point analysis.

Main Methods:

  • A linear reparameterization technique is employed for rank-based estimation.
  • A score-like test using a weighted Cumulative Sum (CUSUM) process is developed for change point detection.
  • Asymptotic properties are derived under null and local alternative models.

Main Results:

  • The proposed rank-based estimate allows simultaneous inference on model parameters and change point location.
  • The score-like test is computationally efficient, requiring only model fitting under the null hypothesis.
  • Methods demonstrate robustness against outliers and heavy-tailed errors in simulations and real data.

Conclusions:

  • The novel rank-based approach provides a robust and efficient tool for change point detection in linear regression.
  • The proposed methods are suitable for applications where data may contain outliers or exhibit heavy-tailed distributions.