Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1149498 | Journal of Statistical Planning and Inference | 2012 | 9 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
L. Mendo,