Efficiency of martingale methods in recapture studies

SUMMARY The asymptotic variances of various estimators of the population size from a recapture study are calculated. The estimation methods compared are maximum likelihood and a class of natural martingale estimators with both time variation and behavioural response. It is found that (i) the martingale methods appropriate for time variation or behavioural response are fully efficient, (ii) there is no loss of efficiency at all in allowing for time variation, (iii) there is large loss of efficiency in allowing for behavioural response, (iv) there is a natural martingale method that allows for both time variation and behavioural response.

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