19 research outputs found
Estimation of a probability in inverse binomial sampling under normalized linear-linear and inverse-linear loss
Sequential estimation of the success probability in inverse binomial
sampling is considered in this paper. For any estimator , 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 and for
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 tends to , and which guarantee that,
for any in , the risk is lower than its asymptotic value. This
allows selecting the required number of successes, , to meet a prescribed
quality irrespective of the unknown . In addition, the proposed estimators
are shown to be approximately minimax when does not deviate too much from
, and asymptotically minimax as tends to infinity when .Comment: 4 figure