Thesis--Bonn. Thesis statement on added t.p. / Includes bibliographical references (p. 53-57).

Thesis (Ph. D.)--University of Iowa, 2007. / Supervisors: George Woodworth, Matthew Bognar. Includes bibliographical references (leaves 72-73).

A novel approach using smoothing cubic splines and point-area deconvolution to estimate the absorption kinetics of linear systems has been investigated. A smoothing cubic spline is employed as an interpolation function since it is superior to polynomials and other functions commonly used for representation of empirical data in several aspects. An advantage of the method is that results obtained from the same data set will be more consistent, irrespective of who runs the program or how many times you run it. In addition, no initial estimates are needed to run the program. The same sampling time or equally spaced measurement of unit impulse response and response of interest is not required. The method is compared with another method by using simulated data containing various degrees of random noise.

In this thesis, two topics in asymptotic statistics and spline functions are studied. / The first one is a study of testing the equality of Sharpe ratios. We compare two approaches to testing for the equality of many Sharpe ratios: the multivariate test of Wright et al. (2014) and Ledoit and Wolf's (2008) pairwise test. Firstly, Ledoit and Wolf's pairwise test is generalized to a multivariate one for direct comparison. We conclude by proposing a modified version that incorporates the Warp-Speed calibration method of Giacomini et al. (2013). The resulting procedure is much less computationally expensive but is comparable in its accuracy. / The second one is a study of the theoretical properties of an exponential weighting aggregated (EWA) penalized spline estimator, where the smoothing parameter is being averaged over an exponential reweighted posterior distribution. We show that the finite sample mean squared error of the EWA estimator is smaller than that of the smooth penalized spline estimator when the smoothing parameter is chosen to be a fixed value. Consistency and asymptotic normality of the EWA estimator are also developed under general situations. / 這篇論文研究了兩個關於漸近統計和樣條函數的話題。 / 其一是在假設檢驗夏普比率的相等性這個問題中的應用。我們首先比較了Wright et al.（2014）的多元檢驗方法和Ledoit & Wolf（2008）的二元檢驗方法。我們先將Ledoit & Wolf (2008)的二元檢驗法拓展到多元層面，以方便比較。最後，我們提出了採用Giacomini et al.（2013）的曲速法修改后的自助抽樣檢驗法。這種方法極大地降低了實際計算成本，同時保持了其準確性。 / 其二是對樣條估計的漸近表現的研究。我們研究了指數權重合計平滑樣條（EWA）估計，這種方法通過貝葉斯法給予平滑參數一個後驗分佈并將其加權合計。我們通過擴展一個oracle不等式驗證了EWA估計的方差比選定了一個平滑參數的一般平滑樣條估計的方差要小。此外，我們還驗證了EWA估計在一般情況下的一致性和漸近正態性。 / Huang, Wei. / Thesis M.Phil. Chinese University of Hong Kong 2014. / Includes bibliographical references (leaves 80-84). / Abstracts also in Chinese. / Title from PDF title page (viewed on 13, September, 2016). / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only.

by Tat-Ming Tso. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (p. 43-45). / Chapter Chapter 1 --- INTRODUCTION --- p.1 / Chapter §1.1 --- Introduction --- p.1 / Chapter §1.2 --- Preconditioned Conjugate Gradient Method --- p.3 / Chapter §1.3 --- Outline of Thesis --- p.3 / Chapter Chapter 2 --- CIRCULANT AND NON-CIRCULANT PRECONDITIONERS --- p.5 / Chapter §2.1 --- Circulant Matrix --- p.5 / Chapter §2.2 --- Circulant Preconditioners --- p.6 / Chapter §2.3 --- Circulant Preconditioners from Kernel Function --- p.8 / Chapter §2.4 --- Non-circulant Band-Toeplitz Preconditioners --- p.9 / Chapter Chapter 3 --- B-SPLINES --- p.11 / Chapter §3.1 --- Introduction --- p.11 / Chapter §3.2 --- New Version of B-splines --- p.15 / Chapter Chapter 4 --- CIRCULANT PRECONDITIONERS CONSTRUCTED FROM B-SPLINES --- p.24 / Chapter Chapter 5 --- NUMERICAL RESULTS AND CONCLUDING REMARKS --- p.28 / Chapter Chapter 6 --- APPLICATIONS TO SIGNAL PROCESSING --- p.37 / Chapter §6.1 --- Introduction --- p.37 / Chapter §6.2 --- Preconditioned regularized least squares --- p.39 / Chapter §6.3 --- Numerical Example --- p.40 / REFERENCES --- p.43

Electroencephalography (EEG) is a valuable tool for clinical and cognitive applications. EEG allows for measuring and imaging of scalp potentials emitted by brain activity and allows researchers to draw conclusions about underlying brain activity and function. However EEG is limited by poor spatial resolution due to various factors. One reason is the fact that EEG electrodes are separated from current sources in the brain by cerebrospinal fluid (CSF), the skull, and the scalp. Unfortunately the conductivities of these tissues are not yet well known which limits the spatial resolution of EEG.Based on prior research, spatial resolution of the EEG can be improved via use of various mathematical techniques that provide increased accuracy of the representation of scalp potentials. One such method is the surface Laplacian. It has been shown to be a direct approach to improving EEG spatial resolution. Yet this approach depends on a geometric head model and much work has been done on assuming the human head to be spherical.In this project, we will develop a mathematical model for ellipsoidal head geometry based on surface Laplacian calculations by Law [1]. The ellipsoidal head model is more realistic to the human head shape and can therefore improve accuracy of the EEG imaging calculations. We will construct a computational program that utilizes the ellipsoidal head geometry in hopes to provide a more accurate representation of data fits compared to the spherical head models. Also, we will demonstrate that the spline surface Laplacian calculations do indeed increase the spatial resolution thereby affording a greater impact to the clinical and cognitive study community involving EEG. / Department of Physics and Astronomy

Although one significant method of interpolation is that of the cubic spline, it has the drawback of occasionally producing undesired inflections in a curve. As a remedy, the spline can mathematically be "stretched" (so to speak) in much the same way that a draftsman's spline could be pulled at its ends while still being anchored at certain points throughout.This thesis will make use of FORTRAN subroutines given in the April, 1974 issue of Communications of the ACM, which have the capability of applying this tension factor to a cublic spline in a graphics package. It will also discuss the necessary modifications which are required before compatibility can be achieved between these subroutines and the Tektronix terminal which is coupled to the DEC-10 here at Ball State University.

Thesis (M.S.)--Ohio University, August, 2000. / Title from PDF t.p.

Thesis (M.S.)--University of Florida, 2004. / Title from title page of source document. Document formatted into pages; contains 34 pages. Includes vita. Includes bibliographical references.

Thesis (Ph. D. in Mathematics)--Vanderbilt University, Aug. 2006. / Title from title screen. Includes bibliographical references.