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ϕ-Divergence Based Procedure for Parametric Change-Point Problems

Abstract

This paper studies the change-point problem for a general parametric, univariate or multivariate family of distributions. An information theoretic procedure is developed which is based on general divergence measures for testing the hypothesis of the existence of a change. For comparing the exact sizes of the new test-statistic using the criterion proposed in Dale (J R Stat Soc B 48–59, 1986), a simulation study is performed for the special case of exponentially distributed random variables. A complete study of powers of the test-statistics and their corresponding relative local efficiencies, is also considered.

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Correspondence to N. Martín.

Additional information

N. Martín, L. Pardo and K. Zografos were partially supported by grant MTM 2012-33740

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Batsidis, A., Martín, N., Pardo, L. et al. ϕ-Divergence Based Procedure for Parametric Change-Point Problems. Methodol Comput Appl Probab 18, 21–35 (2016). https://doi.org/10.1007/s11009-014-9398-3

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  • DOI: https://doi.org/10.1007/s11009-014-9398-3

Keywords

  • Change-point
  • Information criterion
  • Divergence
  • Wald test-statistic
  • General distributions

AMS 2000 Subject Classification

  • Primary 62F03
  • 62F05
  • Secondary 62H15