Aspects of functional data inference and its applications

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dc.contributor.advisorCox, Dennis D.en_US
dc.creatorLee, Jong Sooen_US
dc.date.accessioned2009-06-04T08:46:41Zen_US
dc.date.available2009-06-04T08:46:41Zen_US
dc.date.issued2006en_US
dc.description.abstractWe consider selected topics in estimation and testing of functional data. In many applications of functional data analysis, we aim to compare the sample functional data from two or more populations. However, the raw functional data often contains noise, some of which can be huge outliers. Hence, we must first perform the smoothing and estimation of functional data, but the existing methods for robust smoothing parameter selection are unsatisfactory. We present an efficient way to compute a smoothing parameter which can be generally applied to most robust smoothers. Then, we propose a procedure for testing pointwise difference of functional data in the two-sample framework. Our proposed method is a generalization of Hotelling's T2 test, and we utilize an adaptive truncation technique of Fan and Lin (1998) for dimension reduction and development of the test statistic. We show that our method performs well when compared with the existing testing procedures. Furthermore, we propose a method to detect the significantly different regions between curves. Once we determine that the samples curves from the two or more populations are significantly different overall, we want to look at the local regions of the curves and see where the differences occur. We present a modification of the multiple testing procedure of Westfall and Young (1993) for this testing method. Finally, we apply our proposed methods to the data from the fluorescence spectroscopic device. The fluorescence spectroscopic device is a medical device designed for early detection of cervical cancer, and the output from the device is a functional data, which makes the analysis challenging. The problems posed by this application have motivated the development of the methodologies in the present work, and we demonstrate that our methods work well in this application.en_US
dc.format.extent112 p.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoTHESIS STAT. 2006 LEEen_US
dc.identifier.citationLee, Jong Soo. "Aspects of functional data inference and its applications." (2006) Diss., Rice University. <a href="https://hdl.handle.net/1911/18934">https://hdl.handle.net/1911/18934</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/18934en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectStatisticsen_US
dc.titleAspects of functional data inference and its applicationsen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentStatisticsen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
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