Thesis (Ph. D.)--University of Texas at Austin, 1998. / Vita. Includes bibliographical references (leaves 95-96). Available also in a digital version from Dissertation Abstracts.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1984. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 83-84).

Thesis (Ph. D.)--Rutgers University, 2009. / "Graduate Program in Mathematics." Includes bibliographical references (p. 57-58).

No description available.

Thesis (Ph.D) - Swinburne University of Technology, Faculty of Information & Communication Technologies, 2008. / [A thesis submitted in total fulfillment of the requirements of for the degree of Doctor of Philosophy, Faculty of Information and Communication Technologies, Swinburne University of Technology, 2008]. Typescript. Includes bibliographical references p. 193-201.

Diplomarbeit--Rheinische Friedrich-Wilhelms-Universität, 2003. / Includes bibliographical references (p. 102-103).

The focus of this thesis is extremal dependence among spatial observations. In particular, this research extends the notion of the extremogram to the spatial process setting. Proposed by Davis and Mikosch (2009), the extremogram measures extremal dependence for a stationary time series. The versatility and flexibility of the concept made it well suited for many time series applications including from finance and environmental science. After defining the spatial extremogram, we investigate the asymptotic properties of the empirical estimator of the spatial extremogram. To this end, two sampling scenarios are considered: 1) observations are taken on the lattice and 2) observations are taken on a continuous region in a continuous space, in which the locations are points of a homogeneous Poisson point process. For both cases, we establish the central limit theorem for the empirical spatial extremogram under general mixing and dependence conditions. A high level overview is as follows. When observations are observed on a lattice, the asymptotic results generalize those obtained in Davis and Mikosch (2009). For non-lattice cases, we define a kernel estimator of the empirical spatial extremogram and establish the central limit theorem provided the bandwidth of the kernel gets smaller and the sampling region grows at proper speeds. We illustrate the performance of the empirical spatial extremogram using simulation examples, and then demonstrate the practical use of our results with a data set of rainfall in Florida and ground-level ozone data in the eastern United States. The second part of the thesis is devoted to bootstrapping and variance estimation with a view towards constructing asymptotically correct confidence intervals. Even though the empirical spatial extremogram is asymptotically normal, the limiting variance is intractable. We consider three approaches: for lattice data, we use the circular bootstrap adapted to spatial observations, jackknife variance estimation, and subsampling variance estimation. For data sampled according to a Poisson process, we use subsampling methods to estimate the variance of the empirical spatial extremogram. We establish the (conditional) asymptotic normality for the circular block bootstrap estimator for the spatial extremogram and show L2 consistency of the variance estimated by jackknife and subsampling. Then, we propose a portmanteau style test to check the existence of extremal dependences at multiple lags. The validity of confidence intervals produced from these approaches and a portmanteau style test are demonstrated through simulation examples. Finally, we illustrate this methodology to two data sets. The first is the amount of rainfall over a grid of locations in northern Florida. The second is ground-level ozone in the eastern United States, which are recorded on an irregularly spaced set of stations.

No description available.

Extremal Functions for Graph Linkages and Rooted Minors Paul Wollan 137 pages Directed by: Robin Thomas A graph G is k-linked if for any 2k distinct vertices s_1,..., s_k,t_1,..., t_k there exist k vertex disjoint paths P_1,...,P_k such that the endpoints of P_i are s_i and t_i. Determining the existence of graph linkages is a classic problem in graph theory with numerous applications. In this thesis, we examine sufficient conditions that guarantee a graph to be k-linked and give the following theorems. (A) Every 2k-connected graph on n vertices with 5kn edges is k-linked. (B) Every 6-connected graph on n vertices with 5n-14 edges is 3-linked. The proof method for Theorem (A) can also be used to give an elementary proof of the weaker bound that 8kn edges suffice. Theorem (A) improves upon the previously best known bound due to Bollobas and Thomason stating that 11kn edges suffice. The edge bound in Theorem (B) is optimal in that there exist 6-connected graphs on n vertices with 5n-15 edges that are not 3-linked. The methods used prove Theorems (A) and (B) extend to a more general structure than graph linkages called rooted minors. We generalize the proof methods for Theorems (A) and (B) to find edge bounds for general rooted minors, as well as finding the optimal edge bound for a specific family of bipartite rooted minors. We conclude with two graph theoretical applications of graph linkages. The first is to the problem of determining when a small number of vertices can be used to cover all the odd cycles in a graph. The second is a simpler proof of a result of Boehme, Maharry and Mohar on complete minors in huge graphs of bounded tree-width.

Thesis (Ph. D.)--University of Washington, 1998. / Vita. Includes bibliographical references (p. [59]-61).