Identifiability and One-Sided Inference in the Species Problem
Changxuan Mao and Bruce G. Lindsay
In the classical species problem, the unknown N number of dis- tinct classes in a population can be estimated by sampling individuals from the population. There are several estimation procedures avail- able when the abundance levels of classes are allowed to be di erent. In this paper, it will be shown in a Poisson mixture model that N is identi able with heterogeneous class abundances. However, the only way to construct a con dence interval with a target coverage 1-\alpha is to let the upper con dence limit be in nity. That is, estimation of number of classes is a one-sided inference issue in the sense of Donoho (1988) in that it is possible to obtain sensible lower con dence limits for any target con dence coverage but informative upper con dence limits are not available. Finally, we extend our discussion on identi - ability and one-sided inference issues on population size estimation in capture-recapture studies.
Key WordsNumber of species; Population size; Capture- recapture; One-sided inference; Poisson mixture; Binomial mixture.