Asymptotically optimum estimation of a probability in inverse binomial sampling under general loss functions |
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Authors: | L Mendo |
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Institution: | E.T.S. Ing. Telecomunicación, Universidad Politécnica de Madrid, 28040 Madrid, Spain |
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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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Keywords: | Sequential estimation Asymptotic properties Minimax estimators Inverse binomial sampling |
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