Applied Statistics Commons^™

Addressing The Impact Of Time-Dependent Social Groupings On Animal Survival And Recapture Rates In Mark-Recapture Studies, Alexandru M. Draghici

Electronic Thesis and Dissertation Repository

Mark-recapture (MR) models typically assume that individuals under study have independent survival and recapture outcomes. One such model of interest is known as the Cormack-Jolly-Seber (CJS) model. In this dissertation, we conduct three major research projects focused on studying the impact of violating the independence assumption in MR models along with presenting extensions which relax the independence assumption. In the first project, we conduct a simulation study to address the impact of failing to account for pair-bonded animals having correlated recapture and survival fates on the CJS model. We examined the impact of correlation on the likelihood ratio test (LRT), …

Advances In Semi-Nonparametric Density Estimation And Shrinkage Regression, Hossein Zareamoghaddam

Electronic Thesis and Dissertation Repository

This thesis advocates the use of shrinkage and penalty techniques for estimating the parameters of a regression model that comprises both parametric and nonparametric components and develops semi-nonparametric density estimation methodologies that are applicable in a regression context.

First, a moment-based approach whereby a univariate or bivariate density function is approximated by means of a suitable initial density function that is adjusted by a linear combination of orthogonal polynomials is introduced. Such adjustments are shown to be mathematically equivalent to making use of standard polynomials in one or two variables. Once extended to apply to density estimation, in which case …

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 …

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 …