Abstract
We present a generalized Chao (GC) estimator based on a subject-occasion-specific design matrix. We then extend the GC estimator to (i) external information, in the form of non-linear constraints on subpopulation sizes and (ii) measurement error. For the first, we propose a reparameterization of the estimating equations. As a result, the constrained MLE can be found with no additional computational efforts. For the second we generalize SIMEX procedure to multiple measurement methods. In simulation we show that (even incorrect) external information can substantially decrease the MSE. We illustrate with an application to a whale shark (Rhincodon typus) population, where mostly jouvenile males are observed. We use external information on gender ratio of whale sharks to correct for low catchability of females, and our multivariate SIMEX procedure to correct for measurement error in assessment of shark length. The resulting population size estimates are about 60% larger than the unconstrained–uncorrected counterparts.
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