Type of Document	Dissertation
Author	Auguste, Anna Louisa
Author's Email Address	auguste@stat.fsu.edu
URN	etd-07092006-191704
Title	Estimation From Data Representing a Sample of Curves
Degree	Doctor of Philosophy
Department	Statistics, Department of
Advisory Committee	Advisor Name Title Florentina Bunea Committee Chair Fred Huffer Committee Member Myles Hollander Committee Member Patrick L. Mason Committee Member
Keywords	Confidence Bands Confidence Intervals Nonparametric
Date of Defense	2006-03-29
Availability	unrestricted
Abstract 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.
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