Physical Sciences and Mathematics Commons^™

Flexible Partially Linear Single Index Regression Models For Multivariate Survival Data, Na Lei

Electronic Thesis and Dissertation Repository

Survival regression models usually assume that covariate effects have a linear form. In many circumstances, however, the assumption of linearity may be violated. The present work addresses this limitation by adding nonlinear covariate effects to survival models. Nonlinear covariates are handled using a single index structure, which allows high-dimensional nonlinear effects to be reduced to a scalar term. The nonlinear single index approach is applied to modeling of survival data with multivariate responses, in three popular models: the proportional hazards (PH) model, the proportional odds (PO) model, and the generalized transformation model. Another extension of the PH and PO model …

Asymptotic Theory For Garch-In-Mean Models, Weiwei Liu

Electronic Thesis and Dissertation Repository

The GARCH-in-mean process is an important extension of the standard GARCH (generalized autoregressive conditional heteroscedastic) process and it has wide applications in economics and finance. The parameter estimation of GARCH type models usually involves the quasi-maximum likelihood (QML) technique as it produces consistent and asymptotically Gaussian distributed estimators under certain regularity conditions. For a pure GARCH model, such conditions were already found with asymptotic properties of its QML estimator well understood. However, when it comes to GARCH-in-mean models those properties are still largely unknown. The focus of this work is to establish a set of conditions under which the QML …

Polynomially Adjusted Saddlepoint Density Approximations, Susan Zhe Sheng

Electronic Thesis and Dissertation Repository

This thesis aims at obtaining improved bona fide density estimates and approximants by means of adjustments applied to the widely used saddlepoint approximation. Said adjustments are determined by solving systems of equations resulting from a moment-matching argument. A hybrid density approximant that relies on the accuracy of the saddlepoint approximation in the distributional tails is introduced as well. A certain representation of noncentral indefinite quadratic forms leads to an initial approximation whose parameters are evaluated by simultaneously solving four equations involving the cumulants of the target distribution. A saddlepoint approximation to the distribution of quadratic forms is also discussed. By …

Image Quality Of Energy-Dependent Approaches For X-Ray Angiography, Jesse Evan Tanguay

Electronic Thesis and Dissertation Repository

Digital subtraction angiography (DSA) is an x-ray-based imaging method widely used for diagnosis and treatment of patients with vascular disease. This technique uses subtraction of images acquired before and after injection of an iodinated contrast agent to generate iodine-specific images. While it is extremely successful at imaging structures that are near-stationary over a period of several seconds, motion artifacts can result in poor image quality with uncooperative patients and DSA is rarely used for coronary applications.

Alternative methods of generating iodine-specific images with reduced motion artifacts might exploit the energy-dependence of x-ray attenuation in a patient. This could be performed …

Stochastic Simulation And Spatial Statistics Of Large Datasets Using Parallel Computing, Jonathan Sw Lee

Electronic Thesis and Dissertation Repository

Lattice models are a way of representing spatial locations in a grid where each cell is in a certain state and evolves according to transition rules and rates dependent on a surrounding neighbourhood. These models are capable of describing many phenomena such as the simulation and growth of a forest fire front. These spatial simulation models as well as spatial descriptive statistics such as Ripley's K-function have wide applicability in spatial statistics but in general do not scale well for large datasets. Parallel computing (high performance computing) is one solution that can provide limited scalability to these applications. This is …

Pricing And Hedging Index Options With A Dominant Constituent Stock, Helen Cheyne

Electronic Thesis and Dissertation Repository

In this paper, we examine the pricing and hedging of an index option where one constituents stock plays an overly dominant role in the index. Under a Geometric Brownian Motion assumption we compare the distribution of the relative value of the index if the dominant stock is modeled separately from the rest of the index, or not. The former is equivalent to the relative index value being distributed as the sum of two lognormal random variables and the latter is distributed as a single lognormal random variable. Since these are not equal in distribution, we compare the two models. The …

Modelling Credit Value Adjustment Using Defaultable Options Approach, Sidita Zhabjaku

Electronic Thesis and Dissertation Repository

This thesis calculates Credit Value Adjustment on defaultable options. The prices of default- able European options are computed through analytical, quadrature approximation and Monte Carlo simulations under the assumption of a constant rate of default. Subsequently, we propose to inversely relate the company’s instantaneous rate of default to its underlying stock price, re- sulting in a non-constant rate of default. This allows for a new approach to estimate the default of company different from previous work where default is calculated through historical data. The rationale behind this idea relies on the fact that price of the stock plunges before the …

Seasonal Decomposition For Geographical Time Series Using Nonparametric Regression, Hyukjun Gweon

Electronic Thesis and Dissertation Repository

A time series often contains various systematic effects such as trends and seasonality. These different components can be determined and separated by decomposition methods. In this thesis, we discuss time series decomposition process using nonparametric regression. A method based on both loess and harmonic regression is suggested and an optimal model selection method is discussed. We then compare the process with seasonal-trend decomposition by loess STL (Cleveland, 1979). While STL works well when that proper parameters are used, the method we introduce is also competitive: it makes parameter choice more automatic and less complex. The decomposition process often requires that …

Comparison Of Option Pricing Between Arma-Garch And Garch-M Models, Yi Xi

Electronic Thesis and Dissertation Repository

Option pricing is a major area in financial modeling. Option pricing is sometimes based on normal GARCH models. Normal GARCH models fail to capture the skewness and the leptokurtosis in financial data. The variant GARCH-in-mean (GARCH-M) model is widely used in the option pricing literature. It adds a heteroskedasticity term to the mean equation, which is interpreted as a risk premium, and also incorporates a type of asymmetry.

Our goal is to compare option valuation between GARCH-M and ARMA-GARCH models with normal and non-normal, z-distributed innovations. The models are fitted to the historical return data, and risk neutral measures are …

A New Diagnostic Test For Regression, Yun Shi

Electronic Thesis and Dissertation Repository

A new diagnostic test for regression and generalized linear models is discussed. The test is based on testing if the residuals are close together in the linear space of one of the covariates are correlated. This is a generalization of the famous problem of spurious correlation in time series regression. A full model building approach for the case of regression was developed in Mahdi (2011, Ph.D. Thesis, Western University, ”Diagnostic Checking, Time Series and Regression”) using an iterative generalized least squares algorithm. Simulation experiments were reported that demonstrate the validity and utility of this approach but no actual applications were …

Joint Outcome Modeling Using Shared Frailties With Application To Temporal Streamflow Data, Lihua Li

Electronic Thesis and Dissertation Repository

Recently there has been tremendous interest in the development of tools for joint analysis of longitudinal data and time-to-event data. This has gained emphasis particularly in clinical studies, where longitudinal measurements on a response may be recorded along with a time-to-event outcome. Joint analysis of multiple outcomes beyond longitudinal and survival have also been considered, for example, joint analysis of a variety of generalized linear models including continuous and count data, or continuous and binomial data. With joint analysis of multiple outcomes, the interest may be analysis of one outcome conditional on the others, or, more typically, analysis of all …

Persistence And Anti-Persistence: Theory And Software, Justin Quinn Veenstra

Electronic Thesis and Dissertation Repository

Persistent and anti-persistent time series processes show what is called hyperbolic decay. Such series play an important role in the study of many diverse areas such as geophysics and financial economics. They are also of theoretical interest. Fractional Gaussian noise (FGN) and fractionally-differeneced white noise are two widely known examples of time series models with hyperbolic decay. New closed form expressions are obtained for the spectral density functions of these models. Two lesser known time series models exhibiting hyperbolic decay are introduced and their basic properties are derived. A new algorithm for approximate likelihood estimation of the models using frequency …