Comparison of Confidence Intervals for the TG Estimator in Capture-recapture Data

Abstract

Capture-recapture techniques are very powerful tool and widely used for estimating an elusive target population size. Capture-recapture count data is presented in form of frequencies of frequencies data. They consist of the frequency of unites detected exactly once, twice, and so on, and the frequency of undetected unites is unknown. As consequence, the resulting distribution is a zero-truncated count distribution. The binomial distribution is selected as a simple model if the maximum number of counting occasions is known. It counting occasions are not known in advance, the series of frequencies assumed to be the Poisson distribution. In fact, the target population might be heterogeneous because it has different characteristics, resulting in over or under dispersion based on the basic models. The mixed Poisson, which is the exponential-Poisson mixture model, have been widely used to construct population size estimator for capture-recapture data. The original Turing estimator provides a good performance under the Poisson distribution. Additionally, an extension of Turing estimator, called the Turing-based geometric distribution with non-parametric approach was proposed (TG) for the heterogeneous population. It gives an easy way to estimate the target population size. In this work, we derived uncertainty measures for the TG estimator by considering two sources of variance (M1), and the second way is using only one source of variance (M2). It is emphasised that although the analytic approaches to compute uncertainty measures can be easily used in practice, there are valid asymptotically and requires a large sample size. Therefore, re-sampling approaches, true bootstraps (M3), imputed bootstrap (M4) and reduced bootstrap (M5), are proposed as alternative methods to get uncertainty measures. The study compares performance of variance and confidence interval of paralytics and re-sampling methods by using a simulation study. Overall, the imputed bootstrap is the best choice for estimating variance and constructing confidence interval for the TG estimator. The analytic approach with two sources of variance remains successful to estimate variance and calculate confidence interval in the case of large. It is very clear that the reduced bootstrap and the analytic approach with one source of variance are not appropriate in all situations. For the true bootstrap, the true value of population size is often unknown in nature; therefore, it quite useless for capture-recapture study.