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dc.contributor.supervisor Brewster, John F. (Statistics) en_US
dc.contributor.author Sirski, Monica
dc.date.accessioned 2012-04-10T21:35:35Z
dc.date.available 2012-04-10T21:35:35Z
dc.date.issued 2012-04-10
dc.identifier.uri http://hdl.handle.net/1993/5285
dc.description.abstract We investigate various methods for testing whether two groups of curves are statistically significantly different, with the motivation to apply the techniques to the analysis of data arising from designed experiments. We propose a set of tests based on pairwise differences between individual curves. Our objective is to compare the power and robustness of a variety of tests, including a collection of permutation tests, a test based on the functional principal components scores, the adaptive Neyman test and the functional F test. We illustrate the application of these tests in the context of a designed 2^4 factorial experiment with a case study using data provided by NASA. We apply the methods for comparing curves to this factorial data by dividing the data into two groups by each effect (A, B, . . . , ABCD) in turn. We carry out a large simulation study investigating the power of the tests in detecting contamination, location, and shift effects on unimodal and monotone curves. We conclude that the permutation test using the mean of the pairwise differences in L1 norm has the best overall power performance and is a robust test statistic applicable in a wide variety of situations. The advantage of using a permutation test is that it is an exact, distribution-free test that performs well overall when applied to functional data. This test may be extended to more than two groups by constructing test statistics based on averages of pairwise differences between curves from the different groups and, as such, is an important building-block for larger experiments and more complex designs. en_US
dc.rights info:eu-repo/semantics/openAccess
dc.subject functional data analysis en_US
dc.subject design of experiments en_US
dc.subject permutation test en_US
dc.subject power analysis en_US
dc.title On the statistical analysis of functional data arising from designed experiments en_US
dc.type info:eu-repo/semantics/doctoralThesis
dc.degree.discipline Statistics en_US
dc.contributor.examiningcommittee Leblanc, Alexandre (Statistics) McLeod, Robert (Statistics), Lix, Lisa (Community Health Sciences) Vining, G. Geoffrey (Virginia Tech) en_US
dc.degree.level Doctor of Philosophy (Ph.D.) en_US
dc.description.note May 2012 en_US


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