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arXiv · 1001.3084

Asymptotically optimum estimation of a probability in inverse binomial sampling under general loss functions

Luis Mendo
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Abstract

The optimum quality that can be asymptotically achieved in the estimation of a probability p using inverse binomial sampling is addressed. A general definition of quality is used in terms of the risk associated with a loss function that satisfies certain assumptions. It is shown that the limit superior of the risk for p asymptotically small has a minimum over all (possibly randomized) estimators. This minimum is achieved by certain non-randomized estimators. The model includes commonly used quality criteria as particular cases. Applications to the non-asymptotic regime are discussed considering specific loss functions, for which minimax estimators are derived.

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Luis Mendo. 2010-01-18. Asymptotically optimum estimation of a probability in inverse binomial sampling under general loss functions. https://doi.org/10.1016/j.jspi.2012.03.026

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