Distributions of stopping times in some sequential estimation procedures

Alicja Jokiel-Rokita () and Ryszard Magiera

Metrika: International Journal for Theoretical and Applied Statistics, 2014, vol. 77, issue 5, 617-634

Abstract: A class of sequential estimation procedures is considered in the case when relevant data may become available only at random times. The exact distributions of the optimal stopping time and the number of observations at the moment of stopping are derived in some sequential procedures. The results obtained in an explicit form are applied to derive the expected time of observing the process, the average number of observations and the expected loss of sequential estimation procedures based on delayed observations. The use of the results is illustrated in a special model of normally distributed observations and the Weibull distributed lifetimes. The probabilistic characteristics are also derived for an adaptive sequential procedures and the behavior of the adaptive procedure is compared with the corresponding optimal sequential procedure. Copyright The Author(s) 2014

Keywords: Stopping time; Optimal stopping; Bayes sequential estimation; Distribution of a stopping time; Boundary crossing probability (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:metrik:v:77:y:2014:i:5:p:617-634

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DOI: 10.1007/s00184-013-0456-6

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