Abundance estimation with a categorical covariate subject to missing in continuous-time capture-recapture studies

Abstract

In continuous-time capture-recapture experiments, individual heterogeneity has a large effect on the capture probability. To account for the heterogeneity, we consider an individual covariate, which is categorical and subject to missing. In this article, we develop a general model to summarize three kinds of missing mechanisms, and propose a maximum likelihood estimator of the abundance. A likelihood ratio confidence interval of the abundance is also proposed. We illustrate the proposed methods by simulation studies and a real data example of a bird species prinia subflava in Hong Kong.     

捕获再捕获抽样估计量的模拟研究

目前,捕获再捕获抽样已广泛应用于生物科学、社会科学、生命科学和医学的调查研究中。为此,对捕获再捕获抽样的最常用的Lincoln-Petersen估计量和Chapman估计量进行模拟比较,提出新的有偏估计量,其偏差介于上述两个估计量之间。理论和模拟结果显示：新估计量有时优于其它两个估计量;在实际应用中,当上述两个估计量较难取舍时,新估计量可以作为一个更好的选择。     

A new variant of dual-record population estimation with an application in remote indigenous communities

Dual-record system methods are commonly used as a basis for population estimation. A basic assumption is that the units sampled are drawn only from the population to be estimated. This assumption cannot be met for remote Indigenous communities in Australia. A new variant of dual-record population estimation is presented, which relies on the availability of specific additional information to relax the assumption of perfect frame specification. This variant is applied to two remote Indigenous communities in the Northern Territory of Australia, using locally available data sources. Further theoretical exploration of this method is presented along with possible applications in estimating area-enumerated populations and census coverage.     

Confidence intervals for the closed population size under inverse sampling without replacement

Inverse sampling is an appropriate design for the second phase of capture-recapture experiments which provides an exactly unbiased estimator of the population size. However, the sampling distribution of the resulting estimator tends to be highly right skewed for small recapture samples, so, the traditional Wald-type confidence intervals appear to be inappropriate. The objective of this paper is to study the performance of interval estimators for the population size under inverse recapture sampling without replacement. To this aim, we consider the Wald-type, the logarithmic transformation-based, the Wilson score, the likelihood ratio and the exact methods. Also, we propose some bootstrap confidence intervals for the population size, including the with-replacement bootstrap (BWR), the without replacement bootstrap (BWO), and the Rao–Wu’s rescaling method. A Monte Carlo simulation is employed to evaluate the performance of suggested methods in terms of the coverage probability, error rates and standardized average length. Our results show that the likelihood ratio and exact confidence intervals are preferred to other competitors, having the coverage probabilities close to the desired nominal level for any sample size, with more balanced error rate for exact method and shorter length for likelihood ratio method. It is notable that the BWO and Rao–Wu’s rescaling methods also may provide good intervals for some situations, however, those coverage probabilities are not invariant with respect to the population arguments, so one must be careful to use them.     

A SEMIPARAMETRIC REGRESSION MODEL WITH MISSING COVARIATES IN CONTINUOUS-TIME CAPTURE-RECAPTURE STUDIES

Covariate data were missing when a semiparametric regression model was used to study bird abundance in the Mai Po Sanctuary, Hong Kong. This paper proposes an EM‐type algorithm to estimate the regression parameters for that study. Analytical calculation of the expectation in the EM method is difficult, or even impossible, especially when missing covariates are continuous. A Monte Carlo method is used in the EM algorithm to ease the calculation complexity. Asymptotic variances of the parameter estimates are also derived. Properties of the proposed estimators are assessed through numerical simulations and a real example.     

人口数目估计中的独立双系统估计量研究

利用存在统计相依关系的两份人口登记名单构造的非独立双系统估计量是目前估计总体实际人口数的前沿方法。该估计量由最初用于估计一个区域内的野生动物数目的捕获-再捕获模型移植而来。非独立双系统估计量的一个明显缺陷是低估总体实际人口数。用独立双系统估计量替代非独立双系统估计量属于人口数目估计领域的理论创新研究。采用数理分析与实证分析相结合的方法研究独立双系统估计量及其方差估计量。为便于读者理解,通过一个实证案例全面演示了独立双系统估计量的计算过程。研究表明,独立双系统估计量所估计的人口数平均接近于实际人口数,建议在未来人口数目估计中应用独立双系统估计量。     

The prevalence of heavy narcotics abuse in Sweden in 1992

A case-finding study was carried out in 1992 to determine the prevalence of drug abuse in Sweden. Several authorities in 100 local communities and 59 police districts were selected to participate in the case-finding research. The number of heavy drug abusers was estimated to be 17,000. Heavy drug use is defined as "any intravenous use of drugs, regardless of substance, or any daily or near-daily use of drugs, regardless of the method of administration". The study was designed to make the results comparable to a similar study in 1979 in which the number found was 12,000. According to the studies, the number of heavy drug abusers increased by 5000 between 1979 and 1992. The age distribution shows that the recruitment of abusers has declined, especially among young people.     

关于捕获再捕获抽样的置信区间

捕获再捕获抽样是一种应用广泛的抽样方法。运用随机模拟,研究捕获再捕获抽样的三种估计量的均值、方差、偏度、峰度、利用近似正态分布构造的置信区间的统计性质。改进了估计量的样本方差计算公式,使得利用近似正态分布构造的置信区间更优。     

Multiple recapture methods when sampling without replacement in the last occasion

A technique is presented for estimating the size of a closed population from multiple recapture data when sampling is performed without replacement on the last trapping occasion. The estimator of the population size along with the variance estimator is derived from a log-linear model.     

Bayesian methods for mark-resighting surveys

We consider the problem of estimating the size of a closed population based on the results of a certain type of mark-resighting sampling design. The design is similar to the commonly used multiple capture-recapture design, yet in some cases economically more feasible and easy to use. Sampling is done by first tagging a number of randomly selected animals with visible markers and later randomly sighting them (for instance, for large animals by visually sampling from a helicopter) and counting the number of tagged animals. In this paper, we look at Bayesian methods for point and interval estimation of population size for this design. An example involving estimation of mountain sheep, a couple of simulated examples and simulation studies are given to demonstrate the advantages of the proposed procedure over the other available approximate procedures.