Moment-based nonparametric estimators for the number of classes in a population
Changxuan Mao and Bruce G. Lindsay
Suppose a closed population has in nitely many individuals and is partitioned into unknown N disjoint classes. A random sample is drawn from the population, which may be a Poisson sample or a bi- nomial sample. The issue of interest is the estimation of N. A new nonparametric method is presented in this paper when the population is heterogeneous, which means that the classes vary in abundance. A simple graphical diagnostic is developed to detect the existence of het- erogeneity. An estimator sequence is developed for N, which is based on moment representation of mixture densities and approximation of the total mass of a measure on the positive half of the real line through its higher moments. A bootstrap con dence inference methodology is provided. As illustrations of the procedure, the number of expressed genes in a cDNA library is estimated from a tomato EST dataset and the population size of rabbits is estimated from a capture-recapture dataset.
Key Words Number of species; Population size; Multinomial sample; Capture-recapture; Heterogeneity; Poisson mixture; Binomial mixture; Moment estimator; Mixture identi ability.