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Asymptotically pointwise optimal and asymptotically optimal stopping times in the Bayesian inference

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Abstract

The paper deals with the problem of determining asymptotically pointwise optimal and asymptotically optimal stopping times in the Bayesian inference. The sufficient conditions are given for a family of stopping times to be asymptotically pointwise optimal and asymptotically optimal with respect to a continuous time process. As an example a sequential estimation of the intensity of the Poisson process is considered. Under a gamma prior distribution, an asymptotically pointwise optimal and asymptotically optimal rule is given using a LINEX loss function and the cost c per unit time.

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  1. Institute of Mathematics and Computer Science, Wrocław University of Technology, Wrocław, Poland

    Alicja Jokiel-Rokita

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  1. Alicja Jokiel-Rokita
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Correspondence to Alicja Jokiel-Rokita.

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Jokiel-Rokita, A. Asymptotically pointwise optimal and asymptotically optimal stopping times in the Bayesian inference. Statistical Papers 49, 165–175 (2008). https://doi.org/10.1007/s00362-006-0002-y

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  • DOI: https://doi.org/10.1007/s00362-006-0002-y

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