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Procedures for the Detection of Multiple Changes in Series of Independent Observations

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Part of the book series: Contributions to Statistics ((CONTRIB.STAT.))

Abstract

The paper concerns the problem of detection and identification of one or more change points in a series of independent observations. Procedures based on M-estimatorsand M-residuals are introduced, their limit properties studied and typical simulation results presented.

1990 Mathematics Subject Classification: 62F35, 62G10, 62F03

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References

  1. Antoch J. and Hušková M., Some M-tests for detection of a change in linear models, Proceedings of the 4th Prague Symposium on Asymptotic Statistics (Hušková M. and Mandl P., eds.), Charles University Press, Praha, 1989, pp. 123–136.

    Google Scholar 

  2. Antoch J. and Hušková M., Change point problem, Computational Aspects of Model Choice (Antoch J., ed.), Physica Verlag, Heidelberg, 1992.

    Google Scholar 

  3. Barry D. and Hartigan J. A., A Bayesian analysis for change point problems, Journal of the American Statistical Association 88 (1993), 309–319.

    MathSciNet  MATH  Google Scholar 

  4. Broemling L. D. and Tsurumi H., Econometrics and Structural Change, Series Statistics, vol. 74, M. Dekker, New York, 1986.

    Google Scholar 

  5. Chen X., Inference in a simple change-point problem, Scientia Sinica A 31 (1988), 654–667.

    MATH  Google Scholar 

  6. Csörgő M. and Horváth L., Nonparametric methods for the change point problem, Handbook of Statistics, vol. 7 (Krishnaiah P.R. and Rao C.R., eds.), J. Wiley, New York, 1988, pp. 403–425.

    Google Scholar 

  7. Darkhovskii B.S., Brodskii B.E., A nonparametric method for fastest detection of a change in the mean of a random sequence, Theory of Probability and its Applications 32 (1987), 640–648.

    Article  MathSciNet  Google Scholar 

  8. Darling and Erdös P., A limit theorem for the maximum of normalized sums of independent random variables, Duke Mathematical Journal 23 (1956), 143–155.

    Article  MathSciNet  MATH  Google Scholar 

  9. Deheuvels P. and Révész P., Weak laws for the increments of Wiener processes, Brown-ian bridges, empirical processes and partial sums of i.i.d. r.v.’s., Mathematical Statistics and Probability Theory, vol. A (Puri M.L. et al., eds.),. D. Reidel, Berlin, 1987, pp. 69–88.

    Google Scholar 

  10. Hawkins D. L., A U-I approach to retrospective testing for shifting parameters in a linear model, Communications in Statistics-Theory Methodology 18 (1989), 3117–3134.

    Article  MathSciNet  MATH  Google Scholar 

  11. Hušková M., Recursive M-tests for detection of change, Sequential Analysis 7 (1988 a), 75–90.

    Article  MathSciNet  MATH  Google Scholar 

  12. Hušková M., Tests and estimators for the change point problem based on M-statistics. (submitted)

    Google Scholar 

  13. Hušková M. and Sen. P. K., Nonparametric tests for shift and change in regression at an unknown time point, Statistical Analysis and Forecasting of Economic Structural Change (Hackl P., ed.), Springer-Verlag, New York, 1989, pp. 71–85.

    Chapter  Google Scholar 

  14. Koziol J. A., A note on non-parametric tests for the change-point problem, Biomet-rical. Journal 29 (1987), 323–330.

    MathSciNet  MATH  Google Scholar 

  15. Krishnaiah P. R. and Miao B. Q., Review about estimation of change points, Handbook of Statistics, vol. 7 (Krishnaiah P. R. and Rao R. C, eds.), Elsevier, Amsterdam, 1988, pp. 375–402.

    Google Scholar 

  16. Lombard E., Rank tests for change point problems, Biometrika 74 (1987), 615–624.

    Article  MathSciNet  MATH  Google Scholar 

  17. Shaban S.A., Change point problem and two phase regression: An annotated bibliography, International Statistical Review 48 (1980), 83–93.

    MathSciNet  MATH  Google Scholar 

  18. Steinebach J., Change point and jump estimates in an AMOC renewal model, (this volume)

    Google Scholar 

  19. Wolfe D. A. and Schechtman E., Nonparametric statistical procedures for the change point problem, Journal of Statistical Planning and Inference 9 (1984), 389–396.

    Article  MathSciNet  MATH  Google Scholar 

  20. Zacks S., Survey of classical and Bayesian approaches to the change point problem: Fixed sample and sequential procedures of testing and estimation, Recent Advances in Statistics. Papers in Honor of Herman Chernoff’s Sixtieth Birthday (Rizvi M.H., ed.), Academic Press, New York, 1983, pp. 245–269.

    Google Scholar 

  21. Zacks S., Detection and change-point problem, Handbook of Sequential Analysis (Ghosh B.K. and Sen P.K., eds.), Series Statistics, vol. 118, M. Dekker, New York, 1991.

    Google Scholar 

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© 1994 Springer-Verlag Berlin Heidelberg

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Antoch, J., Hušková, M. (1994). Procedures for the Detection of Multiple Changes in Series of Independent Observations. In: Mandl, P., Hušková, M. (eds) Asymptotic Statistics. Contributions to Statistics. Physica, Heidelberg. https://doi.org/10.1007/978-3-642-57984-4_1

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  • DOI: https://doi.org/10.1007/978-3-642-57984-4_1

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-0770-7

  • Online ISBN: 978-3-642-57984-4

  • eBook Packages: Springer Book Archive

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