Statistica Sinica 27 (2017), 1193-1203
Abstract: The Chao estimator for the number of species plays an important role in conservation biology. We show that its asymptotic variance is not estimable but admits estimable lower and upper bounds. We observe that the pre-existing variance estimator is for the variance lower bound. We propose a bias-adjusted estimator for the variance lower bound. We show that the adjusted Chao estimator in the literature and the proposed adjusted estimator for the variance lower bound are both unbiased in the limit. These findings reinforce the attractiveness of the Chao estimator. Simulation studies and applications are reported.
Key words and phrases: Bio-diversity, population size, species richness.