Abstract: Researchers from a variety of disciplines have studied the problem of estimating the number of distinct classes in a population, known in statistics as the number of species problem. The topic of this paper is the special case of the problem in which the population is finite, its size (or the sampling rate) is known, and auxiliary information correlated to class size is available from sampled classes. We use this information to improve estimation by linking class size to this information via a loglinear model. The parameters of the model are estimated from the sample using conditional maximum likelihood, where the conditioning event is that the class is observed in the sample. The model is then used to estimate the probability of observation for every sampled class, which is in turn used in a Horvitz-Thompson-like estimator of number of classes. The paper shows that the improvement in estimation over other available estimators can be dramatic, especially if the class sizes vary widely. The performance of the estimator degrades when the model is misspecified, but still competes well with alternative estimators.
Key words and phrases: capture-recapture, Horvitz-Thompson estimator, loglinear model, number of classes.