Tests, Point Estimations, and Confidence Sets for a Capture-Recapture Model.

A capture-recapture model that depends on the "catchability" of the individuals in a closed population is considered. A test is derived to decide if the capture efficiencies are the same for two capture attempts. The test given assumes no a priori information about the population and can be used even if one is dealing with relatively small populations. Statistical inferences are drawn about the size of the population. In particular, a family of point estimators for the population size, N, is investigated and compared with the maximum likelihood estimator. Further, confidence intervals for the capture efficiency, is an element of, are combined with joint confidence regions for N and is an element of to obtain confidence intervals for N. It is found that this procedure yields confidence intervals for N whose actual confidence levels are not strongly dependent on the nuisance parameter is an element of. For N less than or equal to 200 the procedure given for finding confidence intervals for N is found to be more satisfactory than the standard approach of simply replacing is an element of with its maximum-likelihood estimate. [ABSTRACT FROM AUTHOR]