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Optimal sequential estimation procedures of a function of a probability of success under LINEX loss

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Abstract

In this paper, we investigate the problem of estimating a function g(p), where p is the probability of success in a sequential sample of independent identically Bernoulli distributed random variables. As a loss associated with estimation we introduce a generalized LINEX loss function. We construct a sequential procedure possessing some asymptotically optimal properties in the case when p tends to zero. In this approach to the problem, the conditions are given, under which the stopping time is asymptotically efficient and normal, and the corresponding sequential estimator is asymptotically normal. The procedure constructed guarantees that its sequential risk is asymptotically equal to a prescribed constant.

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Authors and Affiliations

  1. Institute of Mathematics and Computer Science, Wroclaw University of Technology, Wybrzeże Wyspiańskiego 27, 50-370, Wrocław, Poland

    Jerzy Baran & Ryszard Magiera

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  1. Jerzy Baran
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  2. Ryszard Magiera
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Correspondence to Ryszard Magiera.

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Baran, J., Magiera, R. Optimal sequential estimation procedures of a function of a probability of success under LINEX loss. Stat Papers 51, 511–529 (2010). https://doi.org/10.1007/s00362-008-0137-0

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  • DOI: https://doi.org/10.1007/s00362-008-0137-0

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