Communications for Statistical Applications and Methods

  • 제26권6호
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  • Pages.539-556
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  • 2019
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  • 2287-7843(pISSN)
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  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
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On study for change point regression problems using a difference-based regression model

  • Park, Jong Suk (Department of Statistics, Kyungpook National University) ;
  • Park, Chun Gun (Department of Mathematics, Kyonggi University) ;
  • Lee, Kyeong Eun (Department of Statistics, Kyungpook National University)
  • 투고 : 2019.05.09
  • 심사 : 2019.10.11
  • 발행 : 2019.11.30
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초록

This paper derive a method to solve change point regression problems via a process for obtaining consequential results using properties of a difference-based intercept estimator first introduced by Park and Kim (Communications in Statistics - Theory Methods, 2019) for outlier detection in multiple linear regression models. We describe the statistical properties of the difference-based regression model in a piecewise simple linear regression model and then propose an efficient algorithm for change point detection. We illustrate the merits of our proposed method in the light of comparison with several existing methods under simulation studies and real data analysis. This methodology is quite valuable, "no matter what regression lines" and "no matter what the number of change points".

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참고문헌

  1. Andrews DWK (1993). Tests for parameter instability and structural change with unknown change point, Econometrica, 61, 821-856. https://doi.org/10.2307/2951764
  2. Andrews DWK and Ploberger W (1994). Optimal tests when a nuisance parameter is present only under the alternative, Econometrica, 62, 1383-1414. https://doi.org/10.2307/2951753
  3. Bai J (1997). Estimation of a change point in multiple regressions models, Review of Economics and Statistics, 79, 551-563. https://doi.org/10.1162/003465397557132
  4. Bartels R (1982). The rank version of von Neumann's ratio test for randomness, Journal of the American Statistical Association, 77, 40-46. https://doi.org/10.1080/01621459.1982.10477764
  5. Betts M, Forbes G, and Diamond A (2007). Thresholds in songbird occurrence in relation to landscape structure, Conservation Biology, 21, 1046-1058. https://doi.org/10.1111/j.1523-1739.2007.00723.x
  6. Chen CWS, Chan JSK, Gerlach R, and Hsieh WYL (2011). A comparison of estimators for regression models with change points, Statistics and Computing, 21, 395-414. https://doi.org/10.1007/s11222-010-9177-0
  7. Davison A and Hinkley D (1997). Bootstrap Methods and Their Application, Cambridge University Press.
  8. Fong Y and He Z (2018). Package 'chngpt': Estimation and Hypothesis Testing for Threshold Regression, R package version 2018.7-25. Available from: https://cran.r-project.org/web/packages/chngpt/chngpt.pdf
  9. Fong Y, Huang Y, Gilbert PB, and Permar SR (2017). chngpt: threshold regression model estimation and inference, BMC Bioinformatics, 18:454. https://doi.org/10.1186/s12859-017-1863-x
  10. Hawkins DM (1980). A note on continuous and discontinuous segmented regressions, Technometrics, 22, 443-444. https://doi.org/10.1080/00401706.1980.10486178
  11. Julious SA (2001). Inference and estimation in a changepoint regression problem, The Statistician, 50, 51-61. https://doi.org/10.1111/1467-9884.00260
  12. Kim HJ and Siegmund D (1989). The likelihood ratio test for a changepoint in simple linear regression, Biometrika, 76, 409-423. https://doi.org/10.1093/biomet/76.3.409
  13. Loader CR (1996). Change point estimation using nonparametric regression, The Annals of Statistics, 24, 1667-1678. https://doi.org/10.1214/aos/1032298290
  14. Mateus A and Caeiro F (2015). Package 'randtests': Testing randomness in R, R package version 1.0. Available from: https://cran.r-project.org/web/packages/randtests/randtests.pdf
  15. Muggeo VMR (2003). Estimating regression models with unknown break-points, Statistics in Medicine, 22, 3055-3071. https://doi.org/10.1002/sim.1545
  16. Muggeo VMR (2008). Segmented: An R package to fit regression models with broken-line relationships, R News, 8/1, 20-25.
  17. Muggeo VMR (2017). Package 'segmented': Regression Models with Break-Points/Change-Points Estimation, R package version 0.5-3.0. Available from: https://cran.r-project.org/web/packages/segmented/segmented.pdf
  18. Park CG and Kim I (2019). Robust difference-based outlier detection, Communications in Statistics - Theory Methods, Published online.
  19. Quandt RE (1958). The estimation of the parameters of a linear regression system obeying two separate regimes, Journal of the American Statistical Association, 53, 873-880. https://doi.org/10.1080/01621459.1958.10501484
  20. Ulm K (1991). A statistical methods for assessing a threshold in epidemiological studies, Statistics in Medicine, 10, 341-349. https://doi.org/10.1002/sim.4780100306
  21. Zeileis A, Kleiber C, Kramer W, and Hornik K (2002). Testing and Dating Structural Changes in Exchange Rate Regimes, Computational Statistics and Data Analysis, 54, 1696-1706. https://doi.org/10.1016/j.csda.2009.12.005
  22. Zhou HL and Liang KY (2008). On estimating the change point in generalized linear models, IMS Collections Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen, 1, 305-320. https://doi.org/10.1214/193940307000000239