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On the problems of sequential statistical inference for Wiener processes with delayed observations

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  • Gapeev, Pavel V.

Abstract

We study the sequential hypothesis testing and quickest change-point (or disorder) detection problems with linear delay penalty costs for observable Wiener processes under (constantly) delayed detection times. The method of proof consists of the reduction of the associated delayed optimal stopping problems for one-dimensional diffusion processes to the equivalent free-boundary problems and solution of the latter problems by means of the smooth-fit conditions. We derive closed-form expressions for the Bayesian risk functions and optimal stopping boundaries for the associated weighted likelihood ratio processes in the original problems of sequential analysis.

Suggested Citation

  • Gapeev, Pavel V., 2020. "On the problems of sequential statistical inference for Wiener processes with delayed observations," LSE Research Online Documents on Economics 104072, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:104072
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    References listed on IDEAS

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    Cited by:

    1. Georgy Sofronov & Martin Wendler & Volkmar Liebscher, 2020. "Editorial for the special issue: Change point detection," Statistical Papers, Springer, vol. 61(4), pages 1347-1349, August.
    2. Buonaguidi, B., 2022. "The disorder problem for diffusion processes with the ϵ-linear and expected total miss criteria," Statistics & Probability Letters, Elsevier, vol. 189(C).

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    More about this item

    Keywords

    sequential testing problem; weighted likelihood ratio; quickest change-point (disorder); delayed optimal stopping problem; quickest change-point (disorder) detection problem; change-of-variable formula with local time on curves; free-boundary problem; (time-homogeneous) diffusion process;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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