Abstract: In capture–recapture experiments, covariates collected on individuals, such as body weight and length, are often measured imprecisely or are missing at random. Furthermore, the number of recorded covariate measurements collected on each observed individual is usually equal to or less than the individual's capture frequency. Correcting for multiple error-prone covariates is seldom seen in capture-recapture models and even fewer researchers have considered cases where individual's have no measurements at all. In this paper, we develop an unbiased estimating equation using the conditional score within the capture–recapture framework. We then extend this approach to simultaneously account for both measurement error and missing data using two well-known missing data methods: (1) inverse probability weighting; and (2) multiple imputation. These new methods are shown to yield consistent and asymptotically normal estimators, and the two approaches are shown to be asymptotically equivalent. We evaluated these methods on simulated and real capture–recapture data. Our results show improvements in both precision and efficiency when using the proposed methods.

Key words and phrases: Conditional score, differential measurement errors, inverse probability weighting, missing at random, multiple imputation, population size estimation.