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Limit theorems for change in linear regression

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  • Gombay, Edit
  • Horváth, Lajos

Abstract

We consider some tests to detect a change-point in a multiple linear regression model. The tests are based on the maxima of the weighted cumulative sums processes. The limit distributions may be double exponential or maxima of Gaussian processes depending on the set where the maximum of the weighted cumulative sums of residuals is taken. The design-points can be fixed or random. We also give a few applications of our results.

Suggested Citation

  • Gombay, Edit & Horváth, Lajos, 1994. "Limit theorems for change in linear regression," Journal of Multivariate Analysis, Elsevier, vol. 48(1), pages 43-69, January.
    • Handle: RePEc:eee:jmvana:v:48:y:1994:i:1:p:43-69
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    Citations

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    Cited by:

    1. Lajos Horváth & Curtis Miller & Gregory Rice, 2021. "Detecting early or late changes in linear models with heteroscedastic errors," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 577-609, June.
    2. Jushan, Bai, 1995. "Estimation of multiple-regime regressions with least absolutes deviation," MPRA Paper 32916, University Library of Munich, Germany, revised Feb 1998.
    3. Pouliot, William, 2016. "Robust tests for change in intercept and slope in linear regression models with application to manager performance in the mutual fund industry," Economic Modelling, Elsevier, vol. 58(C), pages 523-534.
    4. Horváth, Lajos & Rice, Gregory & Zhao, Yuqian, 2023. "Testing for changes in linear models using weighted residuals," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    5. Habibi Reza, 2011. "A note on approximating distribution functions of cusum and cusumsq tests," Monte Carlo Methods and Applications, De Gruyter, vol. 17(1), pages 1-10, January.
    6. Michael W. Robbins & Colin M. Gallagher & Robert B. Lund, 2016. "A General Regression Changepoint Test for Time Series Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 670-683, April.
    7. Aurelio Fernández Bariviera & M. Belén Guercio & Lisana B. Martinez, 2014. "Informational Efficiency in Distressed Markets: The Case of European Corporate Bonds," The Economic and Social Review, Economic and Social Studies, vol. 45(3), pages 349-369.
    8. Cui, Junfeng & Wang, Guanghui & Zou, Changliang & Wang, Zhaojun, 2023. "Change-point testing for parallel data sets with FDR control," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).
    9. Lajos Horváth & William Pouliot & Shixuan Wang, 2017. "Detecting at-Most-m Changes in Linear Regression Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(4), pages 552-590, July.

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