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The geometric convergence rate of the classical change-point estimate

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  • Fotopoulos, Stergios B.

Abstract

An analytic method for obtaining optimum rates of convergence for the total variation distances is established. The distance engages the distribution of the maximum likelihood estimate of the change-point in a fixed sample size time ordered data and the distribution of the maximum likelihood estimate of the change-point in an infinite time series data. The method is based purely on probabilistic arguments. Various ideas from random walks, supermartingales, ladder heights, and a recursive sequence of embedded random walks are considered. The optimum rate factor involves the probability of the first passage time to the positive axis.

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  • 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.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:2:p:131-137
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    References listed on IDEAS

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    1. 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.
    2. Stadje, Wolfgang, 2000. "An iterative approximation procedure for the distribution of the maximum of a random walk," Statistics & Probability Letters, Elsevier, vol. 50(4), pages 375-381, December.
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    Cited by:

    1. Kazemi, Mohammad Sadegh & Fotopoulos, Stergios B. & Wang, Xinchang, 2023. "Minimizing online retailers’ revenue loss under a time-varying willingness-to-pay distribution," International Journal of Production Economics, Elsevier, vol. 257(C).

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