Efficiency of the semi-parametric maximum likelihood estimator in generalized case-control studies

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dc.contributor.advisor Lee, Alan en
dc.contributor.author Hirose, Yuichi en
dc.date.accessioned 2007-06-13T04:13:10Z en
dc.date.available 2007-06-13T04:13:10Z en
dc.date.issued 2005 en
dc.identifier THESIS 05-241 en
dc.identifier.citation Thesis (PhD--Statistics)--University of Auckland, 2005 en
dc.identifier.uri http://hdl.handle.net/2292/499 en
dc.description Full text is available to authenticated members of The University of Auckland only. en
dc.description.abstract In this thesis, we investigate the efficiency of the semi-parametric maximum likelihood estimator in the context of generalized case-control studies. We introduce the idea of a multi-sample model and show that it enables us to treat a number of variations of the basic case-control study under the same framework in a natural way. For example, data from a case-control study are a multi-sample, since they consist of two independent samples, one from the case population and one from the control population. Some missing data can also be treated as a multi-sample. We select full data from the full data population and partial data from the other population. Moreover, data gathered using an outcome-dependent two-phase sampling design can also be regarded as a multi-sample. We show that the theory of M-estimation for an i.i.d. model can be extended naturally to multi-sample models, and treat maximum likelihood in these models as a special case of M-estimation. The efficiency of the maximum likelihood estimator can then be studied using the theory of M-estimators in a multi-sample model. Scott & Wild (1997, 2001) use a profile likelihood approach to calculate the semiparametric maximum likelihood estimator in generalized case-control studies. The resulting estimating equations cannot be treated using standard M-estimator theory, since the estimating functions depend on the sample size. We extend the standard treatment of estimating functions to include the derivative of the profile log-likelihood so that the maximum likelihood estimator, the solution to its corresponding estimating equation, is a special case of an M-estimator. We then demonstrate that the semi-parametric MLE is the most efficient among the class of extended M-estimators. en
dc.language.iso en en
dc.publisher ResearchSpace@Auckland en
dc.relation.ispartof PhD Thesis - University of Auckland en
dc.relation.isreferencedby UoA99149156814002091 en
dc.rights Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. en
dc.rights Restricted Item. Available to authenticated members of The University of Auckland. en
dc.rights.uri https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm en
dc.title Efficiency of the semi-parametric maximum likelihood estimator in generalized case-control studies en
dc.type Thesis en
thesis.degree.discipline Statistics en
thesis.degree.discipline Statistics en
thesis.degree.grantor The University of Auckland en
thesis.degree.level Doctoral en
thesis.degree.name PhD en
dc.rights.holder Copyright: The author en

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