Applied Statistics Commons^™

Advances In Portmanteau Diagnostic Tests, Jinkun Xiao

Electronic Thesis and Dissertation Repository

Portmanteau test serves an important role in model diagnostics for Box-Jenkins Modelling procedures. A large number of Portmanteau test based on the autocorrelation function are proposed for a general purpose goodness-of-fit test. Since the asymptotic distributions for the statistics has a complicated form which makes it hard to obtain the p-value directly, the gamma approximation is introduced to obtain the p-value. But the approximation will inevitably introduce approximation errors and needs a large number of observations to yield a good approximation. To avoid some pitfalls in the approximation, the Lin-Mcleod Test is further proposed to obtain a numeric solution to …

Joint Analysis Of Zero-Heavy Longitudinal Outcomes: Models And Comparison Of Study Designs, Erin R. Lundy

Electronic Thesis and Dissertation Repository

Understanding the patterns and mechanisms of the process of desistance from criminal activity is imperative for the development of effective sanctions and legal policy. Methodological challenges in the analysis of longitudinal criminal behaviour data include the need to develop methods for multivariate longitudinal discrete data, incorporating modulating exposure variables and several possible sources of zero-inflation. We develop new tools for zero-heavy joint outcome analysis which address these challenges and provide novel insights on processes related to offending patterns. Comparisons with existing approaches demonstrate the benefits of utilizing modeling frameworks which incorporate distinct sources of zeros. An additional concern in this …

Completely Monotone And Bernstein Functions With Convexity Properties On Their Measures, Shen Shan

Electronic Thesis and Dissertation Repository

The concepts of completely monotone and Bernstein functions have been introduced near one hundred years ago. They find wide applications in areas ranging from stochastic L\'{e}vy processes and complex analysis to monotone operator theory. They have well-known Bernstein and L\'{e}vy-Khintchine integral representations through which there are one-to-one correspondences between them and Radon measures on $[0,\infty)$ or $(0,\infty)$, respectively. In this thesis, we investigate subclasses of completely monotone and Bernstein functions with various convexity properties on their measures. These subclasses have intriguing applications in probability theories and convex analysis.

The convexity properties we investigate include convexity, harmonic convexity and $\beta$-convexity of …

A Spatial Analysis Of Forest Fire Survival And A Marked Cluster Process For Simulating Fire Load, Amy A. Morin

Electronic Thesis and Dissertation Repository

The duration of a forest fire depends on many factors, such as weather, fuel type and fuel moisture, as well as fire management strategies. Understanding how these impact the duration of a fire can lead to more effective suppression efforts as this information can be incorporated into decision support systems used by fire management agencies to help allocate suppression resources. This thesis presents a thorough survival analysis of lightning and people-caused fires in the Intensive fire management zone of Ontario, Canada from 1989 through 2004. The analysis is then extended to investigate spatial patterns across this region using proportional hazards …

Statistical Applications In Wildfire Management And Prediction, Lengyi Han

Electronic Thesis and Dissertation Repository

This thesis develops statistical methods and models and applies them
to problems related to forest fires. The unifying goal of the work is to provide a data analytic basis for quantifying the uncertainty surrounding fire ignition and fire growth which builds on existing theory where possible.

The main body of the thesis is comprised of three research papers. The Fire Weather Index (FWI) plays an important role in fire management and is central to the first two papers. In the first instance, the block bootstrap confidence interval method is used to deal nonparametrically with the dependence in the FWI data. …

Decision Theory Based Models In Insurance And Beyond, Raymond Ye Zhang

Electronic Thesis and Dissertation Repository

Everyday, we make difficult choices under uncertainties. The decision making process becomes even more complicated when more agents get involved: one must consider their interactions and conflicts of interest because the final outcome is based not only on an agent's decision but on everybody's.

In insurance industry, companies try to avoid making large claim payments to policyholders (commonly known as insureds) by purchasing reinsurance policies from reinsurance companies (the reinsurer). Each policy details conditions upon which the reinsurer pays a share of the claim to the insurance company (also known as the cedent or the insurer). To reach an agreement, …

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 …

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 …

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 …

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 …

Generalized Exponential Models With Applications, Iman Mabrouk

Electronic Thesis and Dissertation Repository

We introduce a generalized exponential model whose exact moments and normalizing constant are obtained in terms of Meijer’s generalized hypergeometric G-function. Actually, several widely utilized statistical distributions such as the gamma, Weibull and half-normal constitute particular cases thereof. The generalized inverse Gaussian distribution, which was popularized in the late seventies by Ole Barndor_Neilsen, is also extended by incorporating an additional parameter in its density function, the moments of the resulting distribution being expressed in terms of Bessel functions. A number of data sets were then fitted with diverse exponential-type models for comparison purposes. Additionally, it is shown that the …

Diagnostic Checking, Time Series And Regression, Esam Mahdi

Electronic Thesis and Dissertation Repository

In this thesis, a new univariate-multivariate portmanteau test is derived. The proposed test statistic can be used for diagnostic checking ARMA, VAR, FGN, GARCH, and TAR time series models as well as for checking randomness of series and goodness-of- fit VAR models with stable Paretian errors. The asymptotic distribution of the test statistic is derived as well as a chi-square approximation. However, the Monte-Carlo test is recommended unless the series is very long. Extensive simulation experiments demonstrate the usefulness of this test and its improved power performance compared to widely used previous multivariate portmanteau diagnostic check. The contributed R package …