Robust bent line regression

Feipeng Zhang, Qunhua Li

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We introduce a rank-based bent linear regression with an unknown change point. Using a linear reparameterization technique, we propose a rank-based estimate that can make simultaneous inference on all model parameters, including the location of the change point, in a computationally efficient manner. We also develop a score-like test for the existence of a change point, based on a weighted CUSUM process. This test only requires fitting the model under the null hypothesis in absence of a change point, thus it is computationally more efficient than likelihood-ratio type tests. The asymptotic properties of the test are derived under both the null and the local alternative models. Simulation studies and two real data examples show that the proposed methods are robust against outliers and heavy-tailed errors in both parameter estimation and hypothesis testing.

Original languageEnglish (US)
Pages (from-to)41-55
Number of pages15
JournalJournal of Statistical Planning and Inference
Volume185
DOIs
StatePublished - Jun 1 2017

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Regression line
Change Point
Simultaneous Inference
Linear regression
Reparameterization
Local Alternatives
Parameter estimation
Cumulative Sum
Likelihood Ratio
Hypothesis Testing
Null hypothesis
Asymptotic Properties
Outlier
Null
Parameter Estimation
Simulation Study
Testing
Model
Unknown
Change point

All Science Journal Classification (ASJC) codes

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

Cite this

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Robust bent line regression. / Zhang, Feipeng; Li, Qunhua.

In: Journal of Statistical Planning and Inference, Vol. 185, 01.06.2017, p. 41-55.

Research output: Contribution to journalArticle

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