This dissertation introduces and assesses an algorithm to generate confidence bands for a regression function or a main effect when multiple data sets are available. In particular it proposes to construct confidence bands for different trajectories and then aggregate these to produce an overall confidence band for a mean function. An estimator of the regression function or main effect is also examined. First, nonparametric estimators and confidence bands are formed on each data set separately. Then each data set is in turn treated as a testing set for aggregating the preliminary results from the remaining data sets. The criterion used for this aggregation is either the least squares (LS) criterion or a BIC type penalized LS criterion. The proposed estimator is the average over data sets of these aggregates. It is thus a weighted sum of the preliminary estimators. The proposed confidence band is the minimum L1 band of all the M aggregate bands when we only have a main effect. In the case where there is some random effect we suggest an adjustment to the confidence band. In this case, the proposed confidence band is the minimum L1 band of all the M adjusted aggregate bands. Desirable asymptotic properties are shown to hold. A simulation study examines the performance of each technique relative to several alternate methods and theoretical benchmarks. An application to seismic data is conducted. / A Dissertation submitted to the Department of Statistics in partial fulfillment of
the requirements for the degree of Doctor of Philosophy. / Degree Awarded: Summer Semester, 2006. / Date of Defense: March 29, 2006. / Confidence Bands, Confidence Intervals, Nonparametric / Includes bibliographical references. / Florentina Bunea, Professor Directing Dissertation; Patrick Mason, Outside Committee Member; Myles Hollander, Committee Member; Fred Huffer, Committee Member.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_168400 |
| Contributors | Auguste, Anna L. (authoraut), Bunea, Florentina (professor directing dissertation), Mason, Patrick (outside committee member), Hollander, Myles (committee member), Huffer, Fred (committee member), Department of Statistics (degree granting department), Florida State University (degree granting institution) |
| Publisher | Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text |
| Format | 1 online resource, computer, application/pdf |
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