Mathematics – Statistics Theory
Scientific paper
2010-09-10
Mathematics
Statistics Theory
4 figures
Scientific paper
Sequential estimation of the success probability p in inverse binomial sampling is considered in this paper. For any estimator p^, its quality is measured by the risk associated with normalized loss functions of linear-linear or inverse-linear form. These functions are possibly asymmetric, with arbitrary slope parameters a and b for p^
p respectively. Interest in these functions is motivated by their significance and potential uses, which are briefly discussed. Estimators are given for which the risk has an asymptotic value as p tends to 0, and which guarantee that, for any p in (0,1), the risk is lower than its asymptotic value. This allows selecting the required number of successes, r, to meet a prescribed quality irrespective of the unknown p. In addition, the proposed estimators are shown to be approximately minimax when a/b does not deviate too much from 1, and asymptotically minimax as r tends to infinity when a=b.
Hernando Jose M.
Mendo Luis
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