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Register a new userA new integrated likelihood for estimating population size in dependent dual-record system
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Kiranmoy Chatterjee Dr.
Publication date
2019
fields
Mathematical Statistics
and research's language is
English
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Efficient estimation of population size from dependent dual-record system (DRS) remains a statistical challenge in capture-recapture type experiment. Owing to the nonidentifiability of the suitable Time-Behavioral Response Variation model (denoted as $M_{tb}$) under DRS, few methods are developed in Bayesian paradigm based on informative priors. Our contribution in this article is in developing integrated likelihood function from model $M_{tb}$ based on a novel approach developed by Severini (2007, Biometrika). Suitable weight function on nuisance parameter is derived under the assumption of availability of knowledge on the direction of behavioral dependency. Such pseudo-likelihood function is constructed so that the resulting estimator possess some desirable properties including invariance and negligible prior (or weight) sensitiveness. Extensive simulations explore the better performance of our proposed method in most of the situations than the existing Bayesian methods. Moreover, being a non-Bayesian estimator, it simply avoids heavy computational effort and time. Finally, illustration based on two real life data sets on epidemiology and economic census are presented.
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For Dual-record system, in the context of human population, the popular Chandrasekar-Deming model incorporates only the time variation effect on capture probabilities. How-ever, in practice population may undergo behavioral change after being captured first time. In this paper we focus on the Dual-record system model (equivalent to capture- recapture model with two sampling occasions) with both the time as well as behavioral response variation. The relevant model suffers from identifiability problem. Two approaches are proposed from which approximate Bayes estimates can be obtained using very simple Gibbs sampling strategies. We explore the features of our two proposed methods and their usages depending on the availability (or non-availability) of the information on the nature of behavioral response effect. Extensive simulation studies are carried out to evaluate their performances and compare with few available approaches. Finally, a real data application is provided to the model and the methods.
Motivated by various applications, we consider the problem of homogeneous human population size (N) estimation from Dual-record system (DRS) (equivalently, two-sample capture-recapture experiment). The likelihood estimate from the independent capture-recapture model Mt is widely used in this context though appropriateness of the behavioral dependence model Mtb is unanimously acknowledged. Our primary aim is to investigate the use of several relevant pseudo-likelihood methods profiling N, explicitly for model Mtb. An adjustment over profile likelihood is proposed. Simulation studies are carried out to evaluate the performance of the proposed method compared with Bayes estimate suggested for general capture-recapture experiment by Lee et al. (Statistica Sinica, 2003, vol. 13). We also analyse the effect of possible model mis-specification, due to the use of model Mt, in terms of efficiency and robustness. Finally two real life examples with different characteristics are presented for illustration of the methodologies discussed.
Dual-record system (DRS) (equivalently two sample Capture-recapture experiment) model with time and behavioral response variation, has attracted much attention specifically in the domain of Official Statistics and Epidemiology. The relevant model suffers from parameter identifiability problem and proper Bayesian methodologies could be helpful to overcome the situation. In this article, we have formulated the population size estimation problem in DRS as a missing data analysis under both the known and unknown directional nature of underlying behavioral response effect. Two simple empirical Bayes approaches are proposed and investigated their performances for this complex model along with a fully Bayes treatment. Extensive simulation studies are carried out to compare the performances of these competitive approaches and a real data example is also illustrated. Finally, some features of these methods and recommendations to implement them in practice are explored depending upon the availability of knowledge on the nature of behavioral response effect.
Population size estimation based on capture-recapture experiment under triple record system is an interesting problem in various fields including epidemiology, population studies, etc. In many real life scenarios, there exists inherent dependency between capture and recapture attempts. We propose a novel model that successfully incorporates the possible dependency and the associated parameters possess nice interpretations. We provide estimation methodology for the population size and the associated model parameters based on maximum likelihood method. The proposed model is applied to analyze real data sets from public health and census coverage evaluation study. The performance of the proposed estimate is evaluated through extensive simulation study and the results are compared with the existing competitors. The results exhibit superiority of the proposed model over the existing competitors both in real data analysis and simulation study.
Estimation of population size using incomplete lists (also called the capture-recapture problem) has a long history across many biological and social sciences. For example, human rights and other groups often construct partial and overlapping lists of victims of armed conflicts, with the hope of using this information to estimate the total number of victims. Earlier statistical methods for this setup either use potentially restrictive parametric assumptions, or else rely on typically suboptimal plug-in-type nonparametric estimators; however, both approaches can lead to substantial bias, the former via model misspecification and the latter via smoothing. Under an identifying assumption that two lists are conditionally independent given measured covariate information, we make several contributions. First, we derive the nonparametric efficiency bound for estimating the capture probability, which indicates the best possible performance of any estimator, and sheds light on the statistical limits of capture-recapture methods. Then we present a new estimator, and study its finite-sample properties, showing that it has a double robustness property new to capture-recapture, and that it is near-optimal in a non-asymptotic sense, under relatively mild nonparametric conditions. Next, we give a method for constructing confidence intervals for total population size from generic capture probability estimators, and prove non-asymptotic near-validity. Finally, we study our methods in simulations, and apply them to estimate the number of killings and disappearances attributable to different groups in Peru during its internal armed conflict between 1980 and 2000.
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