A Conditional Generalized Least Squares Method for Estimating the Size of a Closed Population

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Abstract
In the corrected Leslie–DeLury catch-per-unit-effort method, estimation of the corrected cumulative catches causes the underlying model to be an errors-in-covariates structural model with a nondiagonal dispersion matrix. This violates the assumptions of regression and causes the corrected Leslie–DeLury method to give biased estimates of the population size and its variance. We use generalized least squares and a controlled variables design to resolve these difficulties, obtain the minimum-variance unbiased linear estimator, and compute unbiased variance estimates. We apply our method to sockeye salmon fingerlings (Oncorhynchus nerka) netted in a hatchery pond. For these data, arranged according to the controlled variables design, the corrected Leslie–DeLury method underestimates the standard error of the population size by 41%.

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