My dissertation presents a novel statistical method to estimate a sparse signal in functional data and to construct confidence bands for the signal. Existing methods for inference for the mean function in this framework include smoothing splines and kernel estimates. Our methodology involves thresholding a least squares estimator, and the threshold level depends on the sources of variability that exist in this type of data. The proposed estimation method and the confidence bands successfully adapt to the sparsity of the signal. We present supporting evidence through simulations and applications to real datasets. / A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of Doctor of Philosophy.. / Fall Semester, 2008. / October 24, 2008. / Sparse Signal, Functional Data Analysis / Includes bibliographical references. / Florentina Bunea, Professor Co-Directing Dissertation; Marten Wegkamp, Professor Co-Directing Dissertation; Joshua Gert, Outside Committee Member; Xufeng Niu, Committee Member; Myles Hollander, Committee Member.
|Contributors||Ivanescu, Andrada E. (Andrada Eugenia) (authoraut), Bunea, Florentina (professor co-directing dissertation), Wegkamp, Marten (professor co-directing dissertation), Gert, Joshua (outside committee member), Niu, Xufeng (committee member), Hollander, Myles (committee member), Department of Statistics (degree granting department), Florida State University (degree granting institution)|
|Publisher||Florida State University, Florida State University|
|Source Sets||Florida State University|
|Format||1 online resource, computer, application/pdf|
|Rights||This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). The copyright in theses and dissertations completed at Florida State University is held by the students who author them.|
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