We present a generalized Chao (GC)estimator basedonasubject-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) measurementerror. For the first, we propose a reparameterization of the estimating equations. Asa 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 (Rhincodontypus) population, where mostly jouvenile males are observed. We use external informationon gender ratio of whale sharks to correct for low catchability of females, and ourmultivariate 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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• A generalized Chao estimator with measurement error and external information