Physical Sciences and Mathematics Commons^™

On The Distribution Of Quadratic Expressions In Various Types Of Random Vectors, Ali Akbar Mohsenipour

Electronic Thesis and Dissertation Repository

Several approximations to the distribution of indefinite quadratic expressions in possibly singular Gaussian random vectors and ratios thereof are obtained in this dissertation. It is established that such quadratic expressions can be represented in their most general form as the difference of two positive definite quadratic forms plus a linear combination of Gaussian random variables. New advances on the distribution of quadratic expressions in elliptically contoured vectors, which are expressed as scalar mixtures of Gaussian vectors, are proposed as well. Certain distributional aspects of Hermitian quadratic expressions in complex Gaussian vectors are also investigated. Additionally, approximations to the distributions of …

Approximate Methods For Dynamic Portfolio Allocation Under Transaction Costs, Nabeel Butt

Electronic Thesis and Dissertation Repository

The thesis provides robust and efficient lattice based algorithms for solving dynamic portfolio allocation problems under transaction costs. The early part of the thesis concentrates upon developing a toolbox based on multinomial trees. The multinomial trees are shown to provide a reasonable approximation for most popular transaction cost models in the academic literature. The tool, once forged, is implemented in the powerful Mathematica based parallel computing environment. In the second part of the thesis we provide applications of our framework to real world problems. We show re-balancing portfolios is more valuable in an investment environment where the growth and volatility …

Modeling Sequential Event Times Using Family Data, Balakumar Swaminathan

Electronic Thesis and Dissertation Repository

In genetic epidemiology, families harboring certain genetic mutations are predisposed to successive cancers in their lifetime. This thesis aims to provide reliable estimates of relative risk and age-dependent cumulative risks (penetrance) associated with the mutated gene for successive cancers. We develop a statistical framework for modeling sequential event times arising from family data. A shared frailty model is employed to incorporate the dependence between the two event times. Because families are ascertained through non-random sampling, an ascertainment-corrected retrospective likelihood approach is proposed to account for the non-ignorable sampling design. Simulation studies demonstrate that our proposed method provides unbiased and reliable …

The Construction Of Edmond Halley's 1701 Map Of Magnetic Declination, Lori L. Murray

Electronic Thesis and Dissertation Repository

Using the navigational instruments of his time, Edmond Halley collected data during sea voyages of the HMS Paramore. Following these voyages, in 1701 he published a map showing lines of equal magnetic declination. Magnetic declination or variation is the angular difference between magnetic north and geographical or true north for any point on the earth’s surface. The map has been held up by many as an early, and good, example of statistical graphics. Halley did not reveal the data analytic techniques that he used in his map construction and they remain unknown to this day. Using some mathematical tools of …

Simultaneous Confidence Intervals For Risk Ratios In The Many-To-One Comparisons Of Proportions, Jungwon Shin

Electronic Thesis and Dissertation Repository

For many-to-one comparisons of independent binomial proportions using their ratios, we propose the MOVER approach generalizing Fieller's theorem to a ratio of proportions by obtaining variance estimates in the neighbourhood of confidence limits for each proportion. We review two existing methods of inverting Wald and score test statistics and compare their performance with the proposed MOVER approach with score limits and Jeffreys limits for single proportions. As an appropriate multiplicity adjustment incorporating correlations between risk ratios, a Dunnett critical value is computed assuming a common, constant correlation of 0.5 instead of plugging in sample correlation coefficients. The simulation results suggest …

Methods For Shape-Constrained Kernel Density Estimation, Mark A. Wolters

Electronic Thesis and Dissertation Repository

Nonparametric density estimators are used to estimate an unknown probability density while making minimal assumptions about its functional form. Although the low reliance of nonparametric estimators on modelling assumptions is a benefit, their performance will be improved if auxiliary information about the density's shape is incorporated into the estimate. Auxiliary information can take the form of shape constraints, such as unimodality or symmetry, that the estimate must satisfy. Finding the constrained estimate is usually a difficult optimization problem, however, and a consistent framework for finding estimates across a variety of problems is lacking.

It is proposed to find shape-constrained density …

Heterogeneity Issues In The Meta-Analysis Of Cluster Randomization Trials., Shun Fu Chen

Electronic Thesis and Dissertation Repository

An increasing number of systematic reviews summarize results from cluster randomization trials. Applying existing meta-analysis methods to such trials is problematic because responses of subjects within clusters are likely correlated. The aim of this thesis is to evaluate heterogeneity in the context of fixed effects models providing guidance for conducting a meta-analysis of such trials. The approaches include the adjusted Q statistic, adjusted heterogeneity variance estimators and their corresponding confidence intervals and adjusted measures of heterogeneity and their corresponding confidence intervals. Attention is limited to meta-analyses of completely randomized trials having a binary outcome. An analytic expression for power of …

Confidence Intervals For Comparison Of The Squared Multiple Correlation Coefficients Of Non-Nested Models, Li Tan Jr.

Electronic Thesis and Dissertation Repository

Multiple linear regression analysis is used widely to evaluate how an outcome or responsevariable is related to a set of predictors. Once a final model is specified, the interpretation of predictors can be achieved by assessing the relative importance of predictors.

A common approach to predictor importance is to compare the increase in squared multiple correlation for a given model when one predictor is added to the increase when another predictor is added to the same model.

This thesis proposes asymmetric confidence-intervals for a difference between two correlated squared multiple correlation coefficients of non-nested models. These new proceduresare developed by …