Use of the ratio plot in capturerecapture estimation
Boehning, Dankmar, Baksh, M. Fazil, Lerdsuwnasri, Rattana and Gallagher, James (2013) Use of the ratio plot in capturerecapture estimation. Journal of Computational and Graphical Statistics, 22, (1), 135155. (doi:10.1080/10618600.2011.647174).
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Description/Abstract
Statistical graphics are a fundamental, yet often overlooked, set of components in the repertoire of data analytic tools. Graphs are quick and efficient, yet simple instruments of preliminary exploration of a dataset to understand its structure and to provide insight into influential aspects of inference such as departures from assumptions and latent patterns. In this paper, we present and assess a graphical device for choosing a method for estimating population size in capturerecapture studies of closed populations. The basic concept is derived from a homogeneous Poisson distribution where the ratios of neighboring Poisson probabilities multiplied by the value of the larger neighbor count are constant. This property extends to the zerotruncated Poisson distribution which is of fundamental importance in capture–recapture studies. In practice however, this distributional property is often violated. The graphical device developed here, the ratio plot, can be used for assessing specific departures from a Poisson distribution. For example, simple contaminations of an otherwise homogeneous Poisson model can be easily detected and a robust estimator for the population size can be suggested. Several robust estimators are developed and a simulation study is provided to give some guidance on which should be used in practice. More systematic departures can also easily be detected using the ratio plot. In this paper, the focus is on Gammamixtures of the Poisson distribution which leads to a linear pattern (called structured heterogeneity) in the ratio plot. More generally, the paper shows that the ratio plot is monotone for arbitrary mixtures of power series densities.
Item Type:  Article  

Digital Object Identifier (DOI):  doi:10.1080/10618600.2011.647174  
ISSNs:  10618600 (print) 15372715 (electronic) 

Keywords:  chao and robust and generalized chao estimator, closed population, generalized turing estimator, ord plot, poissongamma model, ratio plot, robust turing estimator, structured heterogeneity, turing estimator  
Subjects:  H Social Sciences > HA Statistics  
Divisions:  Faculty of Medicine > Primary Care and Population Sciences Faculty of Social and Human Sciences > Mathematical Sciences > Statistics Faculty of Social and Human Sciences > Southampton Statistical Sciences Research Institute 

ePrint ID:  342535  
Date : 


Date Deposited:  06 Sep 2012 07:42  
Last Modified:  31 Mar 2016 14:33  
URI:  http://eprints.soton.ac.uk/id/eprint/342535 
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