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dc.contributor.advisorMathew, Thomas
dc.contributor.departmentMathematics and Statistics
dc.contributor.programStatistics
dc.creatorSharma, Gaurav
dc.date.accessioned2015-10-14T03:11:38Z
dc.date.available2015-10-14T03:11:38Z
dc.date.issued2010-01-01
dc.description.abstractLikelihood based tests and confidence intervals typically require large sample sizes for their validity. For small sample problems, higher order asymptotics (or small sample asymptotics) appear to be an attractive option to handle parametric inference problems. In the thesis, we will discuss applications of a class of small sample asymptotic procedures, namely, modified signed log-likelihood ratio test (MSLRT) procedures, for the following problems: (i) interval estimation of the consensus mean in inter-laboratory studies, (ii) construction of tolerance intervals in general mixed and random effects models and (iii) inference problems in the combination of multivariate bioassays. In inter-laboratory studies, a fundamental problem of interest is inference concerning the consensus mean, when the measurements are made by several laboratories, which may exhibit different within-laboratory variances, apart from the between laboratory variability. A heteroscedastic one-way random model is very often used to model this scenario. Under such a model, an MSLRT procedure is developed for the interval estimation of the common mean. Furthermore, simulation results are presented to show the accuracy of the proposed confidence interval, especially for small samples. The results are illustrated using an example. The computation of tolerance intervals in mixed and random effects models has not been addressed at all in a general setting, when the data are unbalanced. We derive satisfactory one-sided and two-sided tolerance intervals in such a general scenario, by applying small sample asymptotic procedures. In the case of one-sided tolerance limits, the problem reduces to the interval estimation of a percentile, and accurate confidence intervals are derived using the MSLRT procedure. In the case of two-sided tolerance intervals, the problem does not reduce to an interval estimation problem; however, it is possible to derive an approximate margin of error statistic that is an upper confidence limit for a linear combination of the variance components. For the latter problem, the MSLRT procedures can once again be used in order to arrive at an accurate upper confidence limit. Here, balanced and unbalanced data situations are treated separately, and computational issues are addressed in detail. Bioassays are frequently carried out for the purpose of estimating the relative potency of a drug or material (i.e., test treatment) by comparing its effects with that of a standard treatment on a culture of living cells or a test organism. Data on the relative potencies can sometimes be obtained from several independent experiments, performed at different laboratories or locations. When this is the case, statistical inference problems of interest include testing the homogeneity of the relative potencies, and, if accepted, the interval estimation of the common relative potency. The available literature on the problem assumes a common covariance matrix for the data from the different laboratories or locations. Here we will address the problems in the setup of a MANOVA model for the multivariate bioassay data from the different studies, allowing for different covariance matrices, once again applying the MSLRT procedure. The accuracy of the proposed solutions is assessed based on simulations. Extensive numerical results show that the procedures derived based on higher order asymptotics exhibit satisfactory performance in all three problems regardless of the sample size. The results are illustrated using several examples. The overall conclusion is that the application of higher order asymptotics will result in accurate inference procedures for mixed models and for bioassay problems.
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dc.genredissertations
dc.identifierdoi:10.13016/M20M4C
dc.identifier.other10335
dc.identifier.urihttp://hdl.handle.net/11603/1012
dc.languageen
dc.relation.isAvailableAtThe University of Maryland, Baltimore County (UMBC)
dc.relation.ispartofUMBC Theses and Dissertations Collection
dc.relation.ispartofUMBC Graduate School Collection
dc.relation.ispartofUMBC Student Collection
dc.relation.ispartofUMBC Mathematics and Statistics Department Collection
dc.rightsThis item may be protected under Title 17 of the U.S. Copyright Law. It is made available by UMBC for non-commercial research and education. For permission to publish or reproduce, please see http://aok.lib.umbc.edu/specoll/repro.php or contact Special Collections at speccoll(at)umbc.edu.
dc.sourceOriginal File Name: Sharma_umbc_0434D_10335.pdf
dc.subjectBioassay
dc.subjectInterlaboratory Studies
dc.subjectModified Signed Log Likelihood Ratio Test
dc.subjectSigned Log Likelihood Ratio Test
dc.subjectTolerance Intervals
dc.titleHigher Order Asymptotics: Applications to Mixed Models and Bioassay
dc.typeText


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