  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.
