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dc.contributor.supervisor Mandal, Saumen (Statistics) en_US
dc.contributor.author Chowdhury, Monsur
dc.date.accessioned 2016-09-06T20:01:54Z
dc.date.available 2016-09-06T20:01:54Z
dc.date.issued 2016
dc.identifier.uri http://hdl.handle.net/1993/31637
dc.description.abstract This thesis develops methodologies for the construction of various types of optimal designs with applications in maximum likelihood estimation and factorial structure design. The methodologies are applied to some real data sets throughout the thesis. We start with a broad review of optimal design theory including various types of optimal designs along with some fundamental concepts. We then consider a class of optimization problems and determine the optimality conditions. An important tool is the directional derivative of a criterion function. We study extensively the properties of the directional derivatives. In order to determine the optimal designs, we consider a class of multiplicative algorithms indexed by a function, which satisfies certain conditions. The most important and popular design criterion in applications is D-optimality. We construct such designs for various regression models and develop some useful strategies for better convergence of the algorithms. The remaining thesis is devoted to some important applications of optimal design theory. We first consider the problem of determining maximum likelihood estimates of the cell probabilities under the hypothesis of marginal homogeneity in a square contingency table. We formulate the Lagrangian function and remove the Lagrange parameters by substitution. We then transform the problem to one of maximizing some functions of the cell probabilities simultaneously. We apply this problem to some real data sets, namely, a US Migration data, and a data on grading of unaided distance vision. We solve another estimation problem to determine the maximum likelihood estimation of the parameters of the latent variable models such as Bradley-Terry model where the data come from a paired comparisons experiment. We approach this problem by considering the observed frequency having a binomial distribution and then replacing the binomial parameters in terms of optimal design weights. We apply this problem to a data set from American League Baseball Teams. Finally, we construct some optimal structure designs for comparing test treatments with a control. We introduce different structure designs and establish their properties using the incidence and characteristic matrices. We also develop methods of obtaining optimal R-type structure designs and show how such designs are trace, A- and MV-optimal. en_US
dc.subject Optimal design, directional derivative, maximum likelihood estimation, structure design en_US
dc.title Optimal designs for maximum likelihood estimation and factorial structure design en_US
dc.degree.discipline Statistics en_US
dc.contributor.examiningcommittee Mandal, Saumen (Statistics) Muthukumarana, Saman (Statistics) Yang, Po (Statistics) Appadoo, Srimantoorao (Supply Chain Management) Bhaumik, Dulal (University of Illinois) en_US
dc.degree.level Doctor of Philosophy (Ph.D.) en_US
dc.description.note October 2016 en_US


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