Fully general Chao and Zelterman estimators with application to a whale shark population

We introduce generalized Chao (GC) and Zelterman (GZ) estimators which include individual, time-varying and behavioural effects. Under mild assumptions in the presence of unobserved heterogeneity, the GC estimator asymptotically provides a lower bound for the population size, and is unbiased otherwise. Corrected versions guarantee bounded estimates. In order to include the best set of predictors we propose a 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.