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Statistica Sinica 4(1994), 335-352


SEQUENTIAL UNBIASED ESTIMATION OF THE

NUMBER OF CLASSES IN A POPULATION


Mary C. Christman and Tapan K. Nayak


George Washington University


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.



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