This dissertation presents some topics in spatial statistics and their application in biostatistics and environmental statistics. The
field of spatial statistics is an energetic area in statistics. In Chapter 2 and Chapter 3, the goal is to build subregion models under the
assumption that the responses or the parameters are spatially correlated. For regression models, considering spatially varying coecients is a
reasonable way to build subregion models. There are two different techniques for exploring spatially varying coecients. One is geographically
weighted regression (Brunsdon et al. 1998). The other is a spatially varying coecients model which assumes a stationary Gaussian process for
the regression coecients (Gelfand et al. 2003). Based on the ideas of these two techniques, we introduce techniques for exploring subregion
models in survival analysis which is an important area of biostatistics. In Chapter 2, we introduce modied versions of the Kaplan-Meier and
Nelson-Aalen estimators which incorporate geographical weighting. We use ideas from counting process theory to obtain these modied
estimators, to derive variance estimates, and to develop associated hypothesis tests. In Chapter 3, we introduce a Bayesian parametric
accelerated failure time model with spatially varying coefficients. These two techniques can explore subregion models in survival analysis
using both nonparametric and parametric approaches. In Chapter 4, we introduce Bayesian parametric covariance regression analysis for a
response vector. The proposed method denes a regression model between the covariance matrix of a p-dimensional response vector and auxiliary
variables. We propose a constrained Metropolis-Hastings algorithm to get the estimates. Simulation results are presented to show performance
of both regression and covariance matrix estimates. Furthermore, we have a more realistic simulation experiment in which our Bayesian
approach has better performance than the MLE. Finally, we illustrate the usefulness of our model by applying it to the Google Flu data. In
Chapter 5, we give a brief summary of future work. / A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the
degree of Doctor of Philosophy. / Fall Semester 2017. / November 9, 2017. / Biostatistics, Environment Statistics, Spatial Statistics / Includes bibliographical references. / Fred Huffer, Professor Directing Dissertation; Insu Paek, University Representative; Debajyoti Sinha,
Committee Member; Elizabeth Slate, Committee Member; Jonathan Bradley, Committee Member.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_604973 |
| Contributors | Hu, Guanyu (author), Huffer, Fred W. (Fred William) (professor directing dissertation), Paek, Insu (university representative), Sinha, Debajyoti (committee member), Slate, Elizabeth H. (committee member), Bradley, Jonathan R. (committee member), Florida State University (degree granting institution), College of Arts and Sciences (degree granting college), Department of Statistics (degree granting departmentdgg) |
| Publisher | Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text, doctoral thesis |
| Format | 1 online resource (78 pages), computer, application/pdf |
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