Link-tracing sampling with an initial sequential sample of sites: Estimating the size of a hidden human population

We proposed a modification to the variant of link-tracing sampling suggested by Félix-Medina and Thompson [M.H. Félix-Medina, S.K. Thompson, Combining cluster sampling and link-tracing sampling to estimate the size of hidden populations, Journal of Official Statistics 20 (2004) 19–38] that allows the researcher to have certain control of the final sample size, precision of the estimates or other characteristics of the sample that the researcher is interested in controlling. We achieve this goal by selecting an initial sequential sample of sites instead of an initial simple random sample of sites as those authors suggested. We estimate the population size by means of the maximum likelihood estimators suggested by the above-mentioned authors or by the Bayesian estimators proposed by Félix-Medina and Monjardin [M.H. Félix-Medina, P.E. Monjardin, Combining link-tracing sampling and cluster sampling to estimate the size of hidden populations: A Bayesian-assisted approach, Survey Methodology 32 (2006) 187–195]. Variances are estimated by means of jackknife and bootstrap estimators as well as by the delta estimators proposed in the two above-mentioned papers. Interval estimates of the population size are obtained by means of Wald and bootstrap confidence intervals. The results of an exploratory simulation study indicate good performance of the proposed sampling strategy.     

A simple variance formula for population size estimators by conditioning

This note considers the variance estimation for population size estimators based on capture–recapture experiments. Whereas a diversity of estimators of the population size has been suggested, the question of estimating the associated variances is less frequently addressed. This note points out that the technique of conditioning can be applied here successfully which also allows us to identify sources of variation: the variance due to estimation of the model parameters and the binomial variance due to sampling n units from a population of size N. It is applied to estimators typically used in capture–recapture experiments in continuous time including the estimators of Zelterman and Chao and improves upon previously used variance estimators. In addition, knowledge of the variances associated with the estimators by Zelterman and Chao allows the suggestion of a new estimator as the weighted sum of the two. The decomposition of the variance into the two sources allows also a new understanding of how resampling techniques like the Bootstrap could be used appropriately. Finally, the sample size question for capture–recapture experiments is addressed. Since the variance of population size estimators increases with the sample size, it is suggested to use relative measures such as the observed-to-hidden ratio or the completeness of identification proportion for approaching the question of sample size choice.     

事后调查的理论和它在人口普查修正中的应用

人口普查不可避免地存在误差,如遗漏、重复。为发挥普查的作用,对其结果修正是必要的。一般采用事后调查法修正。事后调查在人口普查结束后进行,主要目的是为修正提供基础数据。普查局利用这些数据,使用捕获再捕获模型,修正人口普查数。     

美国2000年人口普查的准确性和数字评估调查

本文概要地叙述了美国2000年人口普查后所进行的准确性和数字评估调查(A.C.E.调查)。它包括:抽样设计、事后分层、双系统估计等等。     

ESTIMATING POPULATION SIZE FROM CAPTURE-RECAPTURE EXPERIMENTS IN CONTINUOUS TIME

Estimates for the size of a closed population are given for multiple recapture studies in continuous time. The estimates are derived by a method of moments for martingales. An estimate and associated standard error of the population size are derived for a homogeneous population when the capture rates are permitted to depend on time in an unspecified manner. Corresponding results are obtained when the capture rates vary among individuals as well. Explicit expressions are given for these estimates and standard errors which involve only simple computation.     

A Conditionally Unbiased Estimator for the Equal-Catchability Model

ABSTRACT

In this article we reconsider an estimator of population size previously advocated for use when sampling from a population subdivided into different types. We show that it may be usefully adopted in the simple equal-catchability model used in mark-recapture. Unlike the commonly used maximum likelihood estimator, this conditionally unbiased estimator is always finite-valued. Except in situations in which the data contain little relevant information, its performance, in terms of bias and precision, is seen to be at least as good as that of the maximum likelihood estimator. Two estimators of the standard deviation of the conditionally unbiased estimator are considered.     

Bayesian population estimation for small sample capture-recapture data using noninformative priors

One critical issue in the Bayesian approach is choosing the priors when there is not enough prior information to specify hyperparameters. Several improper noninformative priors for capture-recapture models were proposed in the literature. It is known that the Bayesian estimate can be sensitive to the choice of priors, especially when sample size is small to moderate. Yet, how to choose a noninformative prior for a given model remains a question. In this paper, as the first step, we consider the problem of estimating the population size for _Mt$M_{\mathrm{t}}$ model using noninformative priors. The _Mt$M_{\mathrm{t}}$ model has prodigious application in wildlife management, ecology, software liability, epidemiological study, census under-count, and other research areas. Four commonly used noninformative priors are considered. We find that the choice of noninformative priors depends on the number of sampling occasions only. The guidelines on the choice of noninformative priors are provided based on the simulation results. Propriety of applying improper noninformative prior is discussed. Simulation studies are developed to inspect the frequentist performance of Bayesian point and interval estimates with different noninformative priors under various population sizes, capture probabilities, and the number of sampling occasions. The simulation results show that the Bayesian approach can provide more accurate estimates of the population size than the MLE for small samples. Two real-data examples are given to illustrate the method.     

瑞士2000年人口普查的事后调查及其对我国的启示

瑞士首次在2000年人口普查后进行了事后调查。本文介绍这次事后调查样本的抽取、数据的采集、对人口普查时点人口数及其方差的估计。     

APPLICATION OF SEMIPARAMETRIC REGRESSION MODELS IN THE ANALYSIS OF CAPTURE-RECAPTURE EXPERIMENTS

If the capture probabilities in a capture‐recapture experiment depend on covariates, parametric models may be fitted and the population size may then be estimated. Here a semiparametric model for the capture probabilities that allows both continuous and categorical covariates is developed. Kernel smoothing and profile estimating equations are used to estimate the nonparametric and parametric components. Analytic forms of the standard errors are derived, which allows an empirical bias bandwidth selection procedure to be used to estimate the bandwidth. The method is evaluated in simulations and is applied to a real data set concerning captures of Prinia flaviventris, which is a common bird species in Southeast Asia.