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Segmented Model Selection in Quantile Regression Using the Minimum Description Length Principle

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  • Alexander Aue
  • Rex C. Y. Cheung
  • Thomas C. M. Lee
  • Ming Zhong

Abstract

This article proposes new model-fitting techniques for quantiles of an observed data sequence, including methods for data segmentation and variable selection. The main contribution, however, is in providing a means to perform these two tasks simultaneously. This is achieved by matching the data with the best-fitting piecewise quantile regression model, where the fit is determined by a penalization derived from the minimum description length principle. The resulting optimization problem is solved with the use of genetic algorithms. The proposed, fully automatic procedures are, unlike traditional break point procedures, not based on repeated hypothesis tests, and do not require, unlike most variable selection procedures, the specification of a tuning parameter. Theoretical large-sample properties are derived. Empirical comparisons with existing break point and variable selection methods for quantiles indicate that the new procedures work well in practice.

Suggested Citation

  • Alexander Aue & Rex C. Y. Cheung & Thomas C. M. Lee & Ming Zhong, 2014. "Segmented Model Selection in Quantile Regression Using the Minimum Description Length Principle," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1241-1256, September.
    • Handle: RePEc:taf:jnlasa:v:109:y:2014:i:507:p:1241-1256
    DOI: 10.1080/01621459.2014.889022
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    2. Cho, Haeran & Kirch, Claudia, 2024. "Data segmentation algorithms: Univariate mean change and beyond," Econometrics and Statistics, Elsevier, vol. 30(C), pages 76-95.
    3. Alessandro Casini & Pierre Perron, 2018. "Structural Breaks in Time Series," Papers 1805.03807, arXiv.org.
    4. Feiyu Jiang & Zifeng Zhao & Xiaofeng Shao, 2022. "Modelling the COVID‐19 infection trajectory: A piecewise linear quantile trend model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(5), pages 1589-1607, November.
    5. Marie Hušková & Zuzana Prášková, 2014. "Comments on: Extensions of some classical methods in change point analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 265-269, June.
    6. Xu, Bin & Lin, Boqiang, 2016. "A quantile regression analysis of China's provincial CO2 emissions: Where does the difference lie?," Energy Policy, Elsevier, vol. 98(C), pages 328-342.

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