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Maximum likelihood estimation of a change-point for exponentially distributed random variables

Author

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  • Fotopoulos, Stergios
  • Jandhyala, Venkata

Abstract

We consider the problem of estimating the unknown change-point in the parameter of a sequence of independent and exponentially distributed random variables. An exact expression for the asymptotic distribution of the maximum likelihood estimate of the change-point is derived. The analysis is based on the application of Weiner-Hopf factorization identity involving the distribution of ascending and descending ladder heights, and the renewal measure in random walks.

Suggested Citation

  • Fotopoulos, Stergios & Jandhyala, Venkata, 2001. "Maximum likelihood estimation of a change-point for exponentially distributed random variables," Statistics & Probability Letters, Elsevier, vol. 51(4), pages 423-429, February.
    • Handle: RePEc:eee:stapro:v:51:y:2001:i:4:p:423-429
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    Cited by:

    1. Daniela Jarušková, 2018. "Estimating non-simultaneous changes in the mean of vectors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(6), pages 721-743, August.
    2. Fotopoulos, Stergios B., 2009. "The geometric convergence rate of the classical change-point estimate," Statistics & Probability Letters, Elsevier, vol. 79(2), pages 131-137, January.
    3. Venkata Jandhyala & Stergios Fotopoulos & Ian MacNeill & Pengyu Liu, 2013. "Inference for single and multiple change-points in time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 423-446, July.
    4. Fotopoulos, S.B. & Jandhyala, V.K., 2007. "On Hinkley's estimator: Inference about the change point," Statistics & Probability Letters, Elsevier, vol. 77(13), pages 1449-1458, July.

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