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تسجيل مستخدم جديدA Contribution to the Theory Behind the M0 Capture-Recapture Model: An Improved Estimator
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Kyle Vincent
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We explore the use of a sufficient statistic based on the identified members that are obtained for samples that are selected under the $M_0$ capture-recapture closed population model (Schwarz and Seber, 1999). A Rao-Blackwellized version of the estimator based on a sufficient statistic is then presented. We explore the efficiency of the improved estimator via a simulation study. The R code for the simulation is provided in the appendix.
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We explore the use of a sufficient statistic based on the data of samples that are selected under the M_0 capture-recapture closed population model (Schwarz and Seber, 1999). A Rao-Blackwellized version of the estimator based on a sufficient statisti
c is then presented. Though the improvements made on the preliminary capture-recapture estimates are likely to be negligible, this body of work is primarily intended to contribute to the theory around the capture-recapture models. The code for a simulation is provided in the appendix.
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 o
f 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.
Population size estimation based on two sample capture-recapture type experiment is an interesting problem in various fields including epidemiology, pubic health, population studies, etc. The Lincoln-Petersen estimate is popularly used under the assu
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Capture-recapture (CRC) surveys are widely used to estimate the size of a population whose members cannot be enumerated directly. When $k$ capture samples are obtained, counts of unit captures in subsets of samples are represented naturally by a $2^k
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