Estimating the number of classes in a finite population

We use an extension of the generalized jackknife approach of Gray and Schuc any to obtain new nonparametric estimators for the number of classes in a f inite population of known size. We also show that generalized jackknife est imators are closely related to certain Horvitz-Thompson estimators, to an e stimator of Shlosser, and to estimators based on sample coverage. In partic ular, the generalized jackknife approach leads to a modification of Shlosse r's estimator that does not suffer from the erratic behavior of the origina l estimator. The performance of both new and previous estimators is investi gated by means of an asymptotic variance analysis and a Monte Carlo simulat ion study.