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Perpetuities and asymptotic change-point analysis

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  • Baron, Michael
  • Rukhin, Andrew L.

Abstract

The distribution of stochastically discounted sums (perpetuities) is studied. For Bernoulli-type variables a canonical representation of this distribution is obtained, and it is proven to be singular continuous. In the asymptotic setting of the change-point estimation problem the limiting behavior of the posterior distribution is shown to be given by two independent perpetuities.

Suggested Citation

  • Baron, Michael & Rukhin, Andrew L., 2001. "Perpetuities and asymptotic change-point analysis," Statistics & Probability Letters, Elsevier, vol. 55(1), pages 29-38, November.
    • Handle: RePEc:eee:stapro:v:55:y:2001:i:1:p:29-38
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    References listed on IDEAS

    as
    1. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    2. Rukhin Andrew L., 1997. "Change-Point Estimation Under Asymmetric Loss," Statistics & Risk Modeling, De Gruyter, vol. 15(2), pages 141-164, February.
    3. Lumsdaine, Robin L, 1996. "Consistency and Asymptotic Normality of the Quasi-maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models," Econometrica, Econometric Society, vol. 64(3), pages 575-596, May.
    4. Horváth, Lajos, 1989. "The limit distributions of likelihood ratio and cumulative sum tests for a change in a binomial probability," Journal of Multivariate Analysis, Elsevier, vol. 31(1), pages 148-159, October.
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    Cited by:

    1. Pavel Exner & Petr v{S}eba, 2007. "A Markov process associated with plot-size distribution in Czech Land Registry and its number-theoretic properties," Papers 0711.1836, arXiv.org, revised Dec 2007.

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