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Day Of The Week Effect In Returns And Volatility Of The S&P 500 Sector Indices, Juan Liu

Masters Theses

"Previous studies have shown that returns associated with the stock market or foreign exchange's futures show variations across the day of the week. On such study, that employs a modified GARCH model for estimation, shows that returns associated with the S&P 500 stock index is highest on Wednesday and lowest returns on Monday. The same study shows that volatility is highest on Fridays and lowest on Wednesdays. In this study we investigate if this day-of-the-week effect on returns and volatility is present in the different sectors that constitute the S&P 500 index. The data set used provides daily returns from …

Essays On Unit Root Testing In Time Series, Xiao Zhong

Doctoral Dissertations

"Unit root tests are frequently employed by applied time series analysts to determine if the underlying model that generates an empirical process has a component that can be well-described by a random walk. More specifically, when the time series can be modeled using an autoregressive moving average (ARMA) process, such tests aim to determine if the autoregressive (AR) polynomial has one or more unit roots. The effect of economic shocks do not diminish with time when there is one or more unit roots in the AR polynomial, whereas the contribution of shocks decay geometrically when all the roots are outside …

Discrete Analogues Of Some Classical Special Functions, Thomas Joseph Cuchta

Doctoral Dissertations

"Analogues of special functions on time scales are studied with special focus on the time scale 𝕋 = hℤ. Functions investigated in particular include complex monomials, new trigonometric functions, Gaussian bell, Hermite and Laguerre polynomials, Bessel functions, and hypergeometric series"--Abstract, page iii.

Small Sample Saddlepoint Confidence Intervals In Epidemiology, Pasan Manuranga Edirisinghe

Doctoral Dissertations

"In section 1, we develop a novel method of confidence interval construction for directly standardized rates. These intervals involve saddlepoint approximations to the intractable distribution of a weighted sum of Poisson random variables and the determination of hypothetical Poisson mean values for each of the age groups. Simulation studies show that, in terms of coverage probability and length, the saddlepoint confidence interval (SP) outperforms four competing confidence intervals obtained from the moment matching (M8), gamma-based (G1,G4) and ABC bootstrap (ABC) methods.

In section 2, we first consider Brillinger's classical model for a vital rate estimate with a random denominator. We …

Small Sample Umpu Equivalence Testing Based On Saddlepoint Approximations, Renren Zhao

Doctoral Dissertations

"In the first section, we consider small sample equivalence tests for exponentiality. Statistical inference in this setting is particularly challenging since equivalence testing procedures typically require a much larger sample size, in comparison to classical "difference tests", to perform well. We make use of Butler's marginal likelihood for the shape parameter of a gamma distribution in our development of equivalence tests for exponentiality. We consider two procedures using the principle of confidence interval inclusion, four Bayesian methods, and the uniformly most powerful unbiased (UMPU) test where a saddlepoint approximation to the intractable distribution of a canonical sufficient statistic is used. …

Generation And Validation Of Optimal Topologies For Solid Freeform Fabrication, Purnajyoti Bhaumik

Masters Theses

"The study of fabricating topologically optimized parts is presented hereafter. The mapping of topology optimization results for Standard Tessellation Language (STL) writing would enable the solid freeform fabrication of lightweight mechanisms. Aerospace leaders such as NASA, Boeing, Airbus, European Aeronautic Defense And Space Company (EADS), and GE Aero invest in topology optimization research for the production of lightweight materials. Certain concepts such as microstructural homogenization, discretization, and mapping are reviewed and presented in the context of topology optimization. Future biomedical applications of solid freeform fabrication such as organ printing stand to save millions of lives through the robust development of …

On Testing Common Indices For Several Multi-Index Models: A Link-Free Approach, Xuejing Liu

Doctoral Dissertations

"To avoid the curse of dimensionality, and to help us better understand the structure of the high dimensional data, methods for dimension reduction are clearly called for. The common linear dimension reduction techniques for single population include principal component analysis (PCA) which is unsupervised in regression and supervised Partial Least Squares (PLS). Modern sufficient dimension reduction techniques, like the ones we consider, constitute a form of supervised linear dimension reduction which outperform PCA and PLS without the underlying model assumptions.

In practice, we often deal with situations where the same variables are being measured on objects from different groups, and …

Some Combinatorial Applications Of Sage, An Open Source Program, Jessica Ruth Chowning

Masters Theses

"In this thesis, we consider the usefulness of Sage, an online and open-source program, in analyzing permutation puzzles such as the Rubik's cube and a specific combinatorial structure called the projective plane. Many programs exist to expedite calculations in research and provide previously-unavailable solutions; some require purchase, while others, such as Sage, are available for free online. Sage is asked to handle a small permutation puzzle called Swap, and then we explore how it calculates solutions for a Rubik's cube. We then discuss projective planes, Sage's library of functions for dealing with projective planes, and how they relate to the …

Volterra Difference Equations, Nasrin Sultana

Doctoral Dissertations

"This dissertation consists of five papers in which discrete Volterra equations of different types and orders are studied and results regarding the behavior of their solutions are established. The first paper presents some fundamental results about subexponential sequences. It also illustrates the subexponential solutions of scalar linear Volterra sum-difference equations are asymptotically stable. The exact value of the rate of convergence of asymptotically stable solutions is found by determining the asymptotic behavior of the transient renewal equations. The study of subexponential solutions is also continued in the second and third articles. The second paper investigates the same equation using the …