Estimating the number of classes in a finite population

We use an extension of the generalized jackknife approach of Gray and Schucany to obtain new nonparametric estimators for the number of classes in a finite population of known size. We also show that generalized jackknife estimators are closely related to certain Horvitz-Thompson estimators, to an estimator of Shlosser, and to estimators based on sample coverage. In particular, the generalized jackknife approach leads to a modification of Shlosser's estimator that does not suffer from the erratic behavior of the original estimator. The performance of both new and previous estimators is investigated by means of an asymptotic variance analysis and a Monte Carlo simulation study.