Estimating Transition Probabilities from Aggregate Samples Augmented by Haphazard Recaptures

Transition probabilities provide a convenient summary of changes in a categorical trait over time in a population. The difficulties of estimating such probabilities based on only aggregate data from repeated sampling are well known. We give here a method for augmenting aggregate data with haphazard recapture data, which can dramatically improve the estimation precision of transition probabilities. The method requires a rather high sampling fraction to provide sufficient numbers of recaptures. It is based on a generalized nonlinear least squares strategy which yields transition probability estimates preserving their natural parameter space, and which are asymptotically efficient. The asymptotic theory is given under finite population sampling assumptions which are typical in practice.