Tests, Point Estimations, and Confidence Sets for a Capture-Recapture Model
研究了封闭种群中基于个体捕获能力的捕获-再捕获模型，提出了检验两次捕获效率是否相同的统计方法，并比较了多种种群规模点估计量，给出了不依赖干扰参数的置信区间构造方法。
Abstract A capture-recapture model that depends on the “catch-ability” 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, ε, are combined with joint confidence regions for N and ε 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 ε. For N ≤ 200 the procedure given for finding confidence intervals for N is found to be more satisfactory than the standard approach of simply replacing ε with its maximum-likelihood estimate.