Fully General Chao and Zelterman Estimators with Application to a Whale Shark Population

Abstract

Summary We introduce generalized Chao and generalized Zelterman estimators which include individual, time varying and behavioural effects. Under mild assumptions in the presence of unobserved heterogeneity, the generalized Chao estimator asymptotically provides a lower bound for the population size and is unbiased otherwise. Corrected versions guarantee bounded estimates. To include the best set of predictors we propose the biased empirical focused information criterion bFIC. Simulations indicate that bFIC might give considerable improvements over other selection criteria in our context. We illustrate with an original application to size estimation of a whale shark (Rhincodon typus) population in South Ari Atoll, in the Maldives.