Estimating Population Size for Capture-Recapture/Removal Models with Heterogeneity and Auxiliary Information

This dissertation, "Estimating population size for capture-recapture/removal models with heterogeneity and auxiliary information" by Liqun, Xi, 奚李群, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of thesis entitled 'EstimatingPopulationSizeforCapture-Recapture/Removal Models with Heterogeneity and Auxiliary Information' Submitted by Xi Liqun For the Degree of Doctor of Philosophy at The University of Hong Kong in June 2004 This thesis involves two important topics in population size estimation. The first one is how to deal with heterogeneity in population size estimation. Hetero- geneity causes serious bias in estimation. The second one is how to make use of some auxiliary information to improve estimation. For continuous-time capture-recapture experiments, we propose a semipara- metric frailty model in which the capture intensity is allowed to vary with indi- vidual heterogeneity, time and behavioral response. The effect of heterogeneity is modeled as being gamma distributed. The first-capture and recapture intensi- ties are assumed to be in constant proportion but may otherwise vary arbitrarily through time. A likelihood-based approach is proposed to estimate population sizeforthismodelandthesubmodels. Thisapproachisalsoextendedtocapture- recapture experiments with random removals. The asymptotic properties of the estimators are discussed. Simulation studies are conducted to examine the per- formance of the proposed estimation procedures. The estimators are applied to isome real data sets for illustration. For discrete-time capture-recapture experiments, the beta-binomial model for estimating heterogeneous population size is reexamined. It is found that the maximum likelihood estimate (MLE), which was rejected by Burnham (1972, 1978) due to quite unsatisfactorily operating characteristics, works well as long as capture proportion is not small (not less than about 60%). The performance of martingale estimator Lloyd-Yip (1991) is satisfactory but it requires more detailedinformation. Wealsocomparevariousestimatorsforthismodelincluding the conditional maximum likelihood estimate (CMLE), the Gibbs sampler and Metropolis-Hastings algorithm, the jackknife and the sample coverage (Chao, 1989) estimators. In a proportional trapping model proposed by Good et al. (1979), we as- sume capture times are recorded in each trapping occasion (Good's model is a discrete-time removal model without capture times, the resulting estimator is ill-conditioned due to lack of information). With this additional information, maximum likelihood estimate and optimal martingale estimation are studied. The ill-conditioning difficulties are avoided, the estimation is improved. We also extend the model to capture-recapture method. The asymptotic properties of the estimators are derived. Simulation studies are conducted to examine the performance of the proposed estimation procedures. iiIn a continuous-time removal experiment for estimating the size of a popula- tion, we assume that a sub-population size ratio is known. With this additional information, both the maximum likelihood estimate and the optimal martingale estimate of the population size are given. The two estimates are also extended to multiple sub-populations with known size ratios. It is shown that the two estimators are same. The performance of the estimator is compared with that of the maximum likelihood estimate which ignores the information on the known size ratio. The sensitivity of misspecification of the known size ratio is examined. We also compare the simulation results with those based on the correspo