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Tests for multiple change points under ordered alternatives

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Abstract.

We consider the problem of testing the null hypothesis of no change against the alternative of multiple change points in a series of independent observations when the changes are in the same direction. We extend the tests of Terpstra (1952), Jonckheere (1954) and Puri (1965) to the change point setup. We obtain the asymptotic null distribution of the proposed tests. We also give approximations for their limiting critical values and tables of their finite sample Monte Carlo critical values. The results of Monte Carlo power studies conducted to compare the proposed tests with some competitors are reported.

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Authors and Affiliations

  1. Department of Statistics & Operations Research, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait, , , , , , KW

    Emad-Eldin A. A. Aly & Noriah M. Al-Kandari

  2. Department of Statistics, Faculty of Economics & Political Science, Cairo University, Cairo, Egypt, , , , , , EG

    Abd-Elnaser S. Abd-Rabou

Authors
  1. Emad-Eldin A. A. Aly
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  2. Abd-Elnaser S. Abd-Rabou
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  3. Noriah M. Al-Kandari
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Additional information

This research was supported by research grant SS045 of Kuwait University.

Acknowledgments. We wish to thank the two referees for their comments and suggestions which have significantly improved the presentation. We are particularly thankful to one of the referees for suggesting the test statistics Tn1 * (k) and Tn2 * (k).

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Aly, EE., Abd-Rabou, AE. & Al-Kandari, N. Tests for multiple change points under ordered alternatives. Metrika 57, 209–221 (2003). https://doi.org/10.1007/s001840200209

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  • DOI: https://doi.org/10.1007/s001840200209

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