Abstract: We consider unbiased estimation of the number of classes, v, in a population where the classes are equally likely to occur and the parameter space of the number of classes is bounded from above. Among the stopping rules based on a minimal sufficient statistic, the closed and complete plans are characterized. It is shown that v cannot be estimated unbiasedly if the sample size is unbounded, but some finite and closed plans admit unbiased estimators of all functions of v. A general rule for obtaining such estimators is given.
Key words and phrases: Closed sampling plan, completeness, restricted parameter space, stopping rule.