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Capture-recapture estimation and modelling for one-inflated count data

Capture-recapture estimation and modelling for one-inflated count data
Capture-recapture estimation and modelling for one-inflated count data
Capture-recapture methods are used to estimate the unknown size of a target population whose size cannot be reasonably enumerated. This thesis proposes the estimators and the models specifically designed to estimate the size of a population for one-inflated capture-recapture count data allowing for heterogeneity. These estimators can assist with overestimation problems occurring from one-inflation that can be seen in several areas of researches. The estimators are developed under three approaches.
The first approach is based on a modification by truncating singletons and applying the conventional Turing and maximum likelihood estimation approach to the one-truncated geometric data for estimating the parameter p0. These p0 are applied to the Horvitz-Thompson approach for the modified Turing estimator (T_OT) and the modified maximum likelihood estimator (MLE_OT).
The second approach is the model-based approach. It focuses on developing a statistical model that describes the mechanism to generate the extra of count ones. The new estimator MLE_ZTOI is developed from a maximum likelihood approach by using the nested EM algorithm based upon the zero-truncated one-inflated geometric distribution
The last approach focuses on modifying a classical Chao’s estimator to involve the frequency of counts of twos and threes instead of the frequency of counts of ones and twos. The modified Chao estimator (MC) is asymptotic unbiased estimator for a power series distribution with and without one-inflation and provides a lower bound estimator under a mixture of power series distributions with and without one-inflation. The three bias-correction versions of the modified Chao estimator have been developed to reduce the bias when the sample size is small. A variance approximation of MC and MC3 are also constructed by using a conditioning technique.
All of the proposed estimators are assessed through simulation studies. The real data sets are provided for understanding the methodologies.
University of Southampton
Kaskasamkul, Panicha
764f5d81-4b4a-41ad-a35c-f55abcf19e19
Kaskasamkul, Panicha
764f5d81-4b4a-41ad-a35c-f55abcf19e19
Bohning, Dankmar
1df635d4-e3dc-44d0-b61d-5fd11f6434e1

Kaskasamkul, Panicha (2018) Capture-recapture estimation and modelling for one-inflated count data. University of Southampton, Doctoral Thesis, 170pp.

Record type: Thesis (Doctoral)

Abstract

Capture-recapture methods are used to estimate the unknown size of a target population whose size cannot be reasonably enumerated. This thesis proposes the estimators and the models specifically designed to estimate the size of a population for one-inflated capture-recapture count data allowing for heterogeneity. These estimators can assist with overestimation problems occurring from one-inflation that can be seen in several areas of researches. The estimators are developed under three approaches.
The first approach is based on a modification by truncating singletons and applying the conventional Turing and maximum likelihood estimation approach to the one-truncated geometric data for estimating the parameter p0. These p0 are applied to the Horvitz-Thompson approach for the modified Turing estimator (T_OT) and the modified maximum likelihood estimator (MLE_OT).
The second approach is the model-based approach. It focuses on developing a statistical model that describes the mechanism to generate the extra of count ones. The new estimator MLE_ZTOI is developed from a maximum likelihood approach by using the nested EM algorithm based upon the zero-truncated one-inflated geometric distribution
The last approach focuses on modifying a classical Chao’s estimator to involve the frequency of counts of twos and threes instead of the frequency of counts of ones and twos. The modified Chao estimator (MC) is asymptotic unbiased estimator for a power series distribution with and without one-inflation and provides a lower bound estimator under a mixture of power series distributions with and without one-inflation. The three bias-correction versions of the modified Chao estimator have been developed to reduce the bias when the sample size is small. A variance approximation of MC and MC3 are also constructed by using a conditioning technique.
All of the proposed estimators are assessed through simulation studies. The real data sets are provided for understanding the methodologies.

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Published date: March 2018

Identifiers

Local EPrints ID: 424742
URI: https://eprints.soton.ac.uk/id/eprint/424742
PURE UUID: 4cae9e5b-12dd-42b9-ae88-504ec15d13f6
ORCID for Dankmar Bohning: ORCID iD orcid.org/0000-0003-0638-7106

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Date deposited: 05 Oct 2018 11:42
Last modified: 14 Mar 2019 01:37

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