dc.creator Pang, Johnny dc.date.available 2011-02-18T20:17:22Z dc.date.issued 2008-08 dc.identifier.uri http://hdl.handle.net/2346/13432 en_US dc.description.abstract In this dissertation, we will be concerned with the statistical inference regarding linear models with functional data. For the sake of generality these functional data will be considered as sample elements in an abstract infinite dimensional Hilbert space. In the special instance of the one-sample problem, both directly and indirectly observed functions will be included. It should be stressed that the linear model mentioned above each sample elements itself is a function, so that we have more information than in cases where the data consist of a number of sampled function values. In Chapter 1, we will review some useful properties and formulas of arbitrary random variables and Gaussian random variables in Hilbert spaces. It should be noted that a Gaussian measure will be employed as a dominating measure because there doesn't exist a shift invariant (i.e. Lebesgue) measure on an infinite dimensional Hilbert space. In Chapter 2, linear model in Hilbert space will be considered. We will borrow the notation from the univariate linear model and use matrices to arrive at a convenient notation for linear models in Hilbert spaces. We will show that our estimator of the function parameter has approximately a Gaussian distribution for large sample size. In Chapter 3, three special cases of the main model introduced in Chapter $2$ will be considered. First, the simplest version of the one-sample problem in Hilbert spaces will be introduced together with an application of neighborhood hypotheses. Second, the indirect-one-sample problem in Hilbert spaces will be considered. We will exploit the spectral-cut-off type regularized inverse and consider the MISE of the estimator as a means to investigate its quality. In fact, we will prove that the estimator is rate-optimal. Finally, multi-sample problem will be briefly considered along the same lines as the direct one-sample problem. dc.format.mimetype application/pdf dc.language.iso eng dc.publisher Texas Tech University en_US dc.subject Statistics en_US dc.subject Neighbor en_US dc.subject Functional data en_US dc.subject Inverse problem en_US dc.title Some statistical methods for directly and indirecly observed functional data dc.type Dissertation thesis.degree.name Ph.D. thesis.degree.level Doctoral thesis.degree.discipline Mathematics thesis.degree.grantor Texas Tech University thesis.degree.department Mathematics thesis.degree.department Mathematics and Statistics dc.contributor.committeeMember Wang, Alex dc.contributor.committeeMember Paige, Robert dc.contributor.committeeChair Ruymgaart, Frits dc.degree.department Mathematics en_US dc.rights.availability Unrestricted.
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