Environmental and Ecological Statistics manuscript No. (will be inserted by the editor) A generalized Chao estimator with measurement error and external information Francesco Dotto · Alessio Farcomeni Received: date / Accepted: date Abstract We present a generalized Chao (GC) estimator based on a subject- occasion-specific design matrix. We then extend the GC estimator to (i) exter- nal 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 pro- cedure to multiple measurement methods. In simulation we show that (even incorrect) external information can substantially decrease the MSE. We il- lustrate 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. Keywords Chao estimator · SIMEX · external information 1 Introduction The assessment and monitoring of abundance of animal populations is a central issue for conservation, management and in general for comprehension of natu- ral phenomena. It is well acknowledged that exhaustive enumeration of mem- bers of a population of interest is very often impossible. Hence population size is almost always estimated. This can be done for instance by means of distance sampling, mark-recapture or other kind of experiments. See for instance Mc- Crea and Morgan (2014) among many possible references. Capture-recapture experiments for closed populations are based on repeated identification of sub- jects within a population of interest. The information on subjects identified F. Dotto · A. Farcomeni E-mail: alessio.farcomeni@uniroma1.it Sapienza - University of Rome