Abstract: We consider the unbiased estimation of the number of classes, v, in a population when the classes are equally likely to occur. 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 bounded; but unbounded, closed and complete plans admit best unbiased estimators of all functions of v. A general rule for obtaining such estimators is given. It is also shown that without any assumptions about the class probabilities, v cannot be estimated unbiasedly.
Key words and phrases: Sufficiency, completeness, stopping rule, closed sampling plan.