Digital Commons Network^™

Computationally Efficient Specifications Of Spatial Point Process Models And Spatio-Temporal Gaussian Models: Combining Remote Sensing Drivers With Geospatial Disease Case Data To Enhance Geographic Epidemiology, Beth Louise Ziniti

Doctoral Dissertations

In this dissertation, the flexibility of Bayesian hierarchical models specified using a latent Gaussian Markov Random Field (GMRF) are evaluated for use in analyzing large complex spatial and spatio-temporal data with the goal of contributing to an interdisciplinary effort of developing an eco-epidemiological model that quantifies the relationship between remotely sensed water quality and the incidence of ALS (Amyotrophic Lateral Sclerosis or Lou Gehrig’s Disease) over large areas such as Northern New England (NNE).

In particular, a Log-Gaussian Cox Process (LGCP) specified by the logarithm of a GMRF on a regular lattice is shown to allow for simultaneous estimation of …

Extreme Value Theory: Applications To Estimation Of Stochastic Traffic Capacity And Statistical Downscaling Of Precipitation Extremes, Eric Matthew Laflamme

Doctoral Dissertations

This work explores two applications of extreme value analysis. First, we apply EV techniques to traffic stream data to develop an accurate distribution of capacity. Data were collected by the NHDOT along Interstate I93, and two adjacent locations in Salem, NH were examined. Daily flow maxima were used to estimate capacity, and data not associated with daily breakdown were deemed censored values. Under this definition, capacity values are approximated by the generalized extreme value (GEV) distribution for block maxima. To address small sample sizes and the presence of censoring, a Bayesian framework using semi-informative priors was implemented. A simple cross …

On Wavelet-Based Testing For Serial Correlation Of Unknown Form Using Fan's Adaptive Neyman Method, Shan Yao

Doctoral Dissertations

Test procedures for serial correlation of unknown form with wavelet methods are investigated in this dissertation. The new wavelet-based consistent test is motivated using Fan's (1996) canonical multivariate normal hypothesis testing model. In our framework, the test statistic relies on empirical wavelet coefficients of a wavelet-based spectral density estimator. We advocate the choice of the simple Haar wavelet function, since evidence demonstrates that the choice of the wavelet function is not critical. Under the null hypothesis of no serial correlation, the asymptotic distribution of a vector of empirical wavelet coefficients is derived, which is the multivariate normal distribution in the …

Models And Methods For Computationally Efficient Analysis Of Large Spatial And Spatio-Temporal Data, Chengwei Yuan

Doctoral Dissertations

With the development of technology, massive amounts of data are often observed at a large number of spatial locations (n). However, statistical analysis is usually not feasible or not computationally efficient for such large dataset. This is the so-called "big n problem".

The goal of this dissertation is to contribute solutions to the "big n problem". The dissertation is devoted to computationally efficient methods and models for large spatial and spatio-temporal data. Several approximation methods to "the big n problem" are reviewed, and an extended autoregressive model, called the EAR model, is proposed as a parsimonious model that accounts for …

Wavelet Regression With Long Memory Infinite Moving Average Errors, Juan Liu

Doctoral Dissertations

For more than a decade there has been great interest in wavelets and wavelet-based methods. Among the most successful applications of wavelets is nonparametric statistical estimation, following the pioneering work of Donoho and Johnstone (1994, 1995) and Donoho et al. (1995). In this thesis, we consider the wavelet-based estimators of the mean regression function with long memory infinite moving average errors, and investigate the rates of convergence of estimators based on thresholding of empirical wavelet coefficients. We show that these estimators achieve nearly optimal minimax convergence rates within a logarithmic term over a large class of non-smooth functions that involve …

Contributions To Modeling And Computer Efficient Estimation For Gaussian Space -Time Processes, Veronica Pocsik Hupper

Doctoral Dissertations

This thesis research provides several contributions to computer efficient methodology for estimation with space-time data. First we propose a parsimonious class of computer-efficient Gaussian spatial interaction models that includes as special cases CAR and SAR-like models. This extended class is capable of modeling smooth spatial random fields. We show that, for rectangular lattices, this class is equivalent to higher-order Markov random fields. Thus we capture the computational advantage of iterative updating of Markov random fields, while at the same time provide the possibility of simple interpretation of smooth spatial structure.

This class of spatial models is defined via a spatial …

Dynamic Analysis Of Unevenly Sampled Data With Applications To Statistical Process Control, Laura Ann Mcsweeney

Doctoral Dissertations

Dynamic analysis involves describing how a process changes over time. Applications of this type of analysis can be implemented in industrial settings in order to control manufacturing processes and recognize when they have changed significantly. The primary focus of this work is to construct methods to detect the onset of periodic behavior in a process which is being monitored using a scheme where data is sampled unevenly.

Techniques that can be used to identify statistically significant periodic structure using the periodogram will be reviewed and developed. The statistical properties of the periodogram for unevenly sampled data will be calculated. These …

New Methods For Modeling Accelerated Life Test Data, Michelle Hopkins Capozzoli

Doctoral Dissertations

An accelerated life test (ALT) is often used to obtain timely information for highly reliable items. The increased use of ALTs has resulted in nontraditional reliability data which can not be analyzed with standard statistical methodologies. I propose new methods for analyzing ALT data for studies with (1) two independent populations, (2) paired samples and (3) limited failure populations (LFP). Here, the Weibull distribution, which can accommodate a variety of failure rates, is assumed for the models I develop. For case (1), a parametric hypothesis test, a Bayesian analysis and a test using partial likelihood are proposed and discussed. For …

Ecological Database Development And Analyses Of Soil Variability In Northern New England, Michael Anayo Okoye

Doctoral Dissertations

The 1983 Forest Inventory and Analysis (FIA) data of the states of Maine, New Hampshire and Vermont (the study area) contain large amounts of field-measurements of many ecologically important variables. Despite the vast potential usefulness of the FIA data for scientific research, the data were until now, literally unused except for a few administrative purposes, because of problems in the way the data were organized, summarized, and coded for storage. The primary objective of this research was to solve the problems that had thus precluded these FIA data from use in scientific applications, and present the data in a form …

The Association Between Arbitrage Pricing Theory Risk Measures And Traditional Accounting Variables, Theophanis Stratopoulous

Doctoral Dissertations

According to the Arbitrage Pricing Theory (APT), actual security returns depend on a variety of pervasive economic and financial risk factors; as well as firm or industry specific influences. The sensitivity of an asset's returns to unanticipated changes in the pervasive risk factors reflects the security's measure of systematic risk. In equilibrium, the expected security return is a linear function of the sensitivities of actual security returns to unanticipated changes in the pervasive risk factors.

The APT does not specify the number or the nature of the pervasive risk factors. Factor analysis of stock returns can be used to determine …

Money, Income And Causality: An Open Economy Reexamination, El-Hachemi Aliouche

Doctoral Dissertations

The positive relationship between the rate of growth of the money supply and the rate of growth of aggregate income is a widely accepted principle in macroeconomics. However, the direction of the causality between these two variables has been an enduring subject of controversy.

Recent developments in time series analysis, particularly those relating to the concepts of integration and cointegration, and the stationary nature of economic time series, promise to help settle the debate on the statistical relationship between money supply growth and income growth. Most of the recent work on this issue, however, has been confined to a closed …

Dynamic Probabilistic Systems With Continuous Parameter Markov Chains And Semi-Markov Processes, Christopher Tin Htun Lee

Doctoral Dissertations

No abstract provided.