Reduced bias prediction regions and estimators of the original response when using data transformations

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dc.contributorAdams, Benjamin Michael
dc.contributorChakraborti, Subhabrata
dc.contributorMelnykov, Volodymyr
dc.contributorHardy, David E.
dc.contributor.advisorPerry, Marcus B.
dc.contributor.authorWalker, Michael
dc.contributor.otherUniversity of Alabama Tuscaloosa
dc.date.accessioned2017-04-26T14:23:50Z
dc.date.available2017-04-26T14:23:50Z
dc.date.issued2015
dc.descriptionElectronic Thesis or Dissertationen_US
dc.description.abstractInitially motivated by electron microscopy experiments, we develop an approximate prediction interval on the univariate response variable Y, where it is assumed that a normal-theory linear model is fit using a transformed version of Y, and the transformation type is contained in the Box-Cox family. Further motivated by A-10 single-engine climb experiments, we then develop an approximate prediction interval on the univariate response Y, in which a linear model is fit using a transformed version of Y, contained in the Manly exponential family. For each case, we derive a closed-form approximation to the kth moment of the original response variable Y, which is then used to estimate the mean and variance of Y, given parameter estimates obtained from fitting the model in the transformed domain. Chebychev’s inequality is then used to construct a 100(1 − α)% prediction interval estimator on Y based on these mean and variance estimators. Extended data obtained from the A-10 single-engine climb experiments motivates the development of prediction regions in the original domain of a q-variate response vector Y through the use of multivariate extensions of both the Box-Cox power transformation and the Manly exponential transformation. For each transformation, we derive closed-form approximations to the kth moment of each original response Y, as well as a closed-form approximation to E(Yi Yi'), which are used to estimate the mean and variance of each Y and the covariance between them, given parameter estimates obtained from fitting the model in the transformed domain. Exploiting two multivariate analogs of Chebyshev’s inequality, we construct an approximate 100(1 − α)% prediction sphere and ellipsoid on the original response vector Y.en_US
dc.format.extent139 p.
dc.format.mediumelectronic
dc.format.mimetypeapplication/pdf
dc.identifier.otheru0015_0000001_0002058
dc.identifier.otherWalker_alatus_0004D_12372
dc.identifier.urihttp://ir.ua.edu/handle/123456789/3024
dc.languageEnglish
dc.language.isoen_US
dc.publisherUniversity of Alabama Libraries
dc.relation.hasversionborn digital
dc.relation.ispartofThe University of Alabama Electronic Theses and Dissertations
dc.relation.ispartofThe University of Alabama Libraries Digital Collections
dc.rightsAll rights reserved by the author unless otherwise indicated.en_US
dc.subjectStatistics
dc.titleReduced bias prediction regions and estimators of the original response when using data transformationsen_US
dc.typethesis
dc.typetext
etdms.degree.departmentUniversity of Alabama. Department of Information Systems, Statistics, and Management Science
etdms.degree.disciplineApplied Statistics
etdms.degree.grantorThe University of Alabama
etdms.degree.leveldoctoral
etdms.degree.namePh.D.
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