The project aims to estimate the size of an elusive target population. The proposed model is developed to extend the Lincoln- Petersen estimator relying on a two-source situation and binary source/listing variables to non-binary source/listing variables. We consider a bivariate count variable where counts are used to summarize how often a unit was identified from source/list 1 and source/list 2. A mixture model is presented to model unobserved population heterogeneity. Independence of two sources is assumed by conditioning on a homogeneous component leading to discrete mixtures of bivariate, conditional independent Poisson model. The EM algorithm is discussed for maximum likelihood estimation. The model is selected on the basis of Bayesian Information Criterion (BIC). The gradient function is developed to detect candidates to be non parametric maximum likelihood estimator (NPMLE) and then incorporated into the EM algorithm leading to the EM algorithm with gradient function update. Since the gradient function exploits substantially the concavity of the likelihood, we assure that the resulting NPMLE is the global maximum. As an application, estimating the number of drug users in Bangkok, Thailand is examined using the proposed model. A likelihood framework is intrigued by exploring association between unconditional and conditional MLE. Profile mixture likelihood is utilized to tackle unconditional maximum likelihood. Confidence interval estimation for population size is derived based upon the profile mixture likelihood. To allow more flexibility in unobserved population heterogeneity, a continuous mixing distribution is incorporated into the model. We consider Gamma-mixtures of the Poisson distribution and propose two new estimators of the population size in the spirit of the maximum likelihood estimation and the Turing estimator based on the bivariate, independent Geometric model. Estimating associated variances of these estimators is addressed by means of the conditioning technique. The generalised Chao estimator is developed on the basis of the monotonicity of the power series densities. We formulate a lower bound estimator for the number of units belonging to a shared population. The proposed lower bound estimator is applied to estimate the size of a drug use population in which drug users take two drugs such as heroin and methamphetamine at the same time.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:578016 |
| Date | January 2012 |
| Creators | Lerdsuwansri, Rattana |
| Publisher | University of Reading |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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