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Spatial Models with Specific Error Structures

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Date Issued:
2019
Abstract/Description:
The purpose of this dissertation is to study the first order autoregressive model in the spatial context with specific error structures. We begin by supposing that the error structure has a long memory in both the i and the j components. Whenever the model parameters alpha and beta equal one, the limiting distribution of the sequence of normalized Fourier coefficients of the spatial process is shown to be a function of a two parameter fractional Brownian sheet. This result is used to find the limiting distribution of the periodogram ordinate of the spatial process under the null hypothesis that alpha equals one and beta equals one. We then give the limiting distribution of the normalized Fourier coefficients of the spatial process for both a moving average and autoregressive error structure. Two cases of autoregressive errors are considered. The first error model is autoregressive in one component and the second is autoregressive in both components. We show that the normalizing factor needed to ensure convergence in distribution of the sequence of Fourier coefficients is different in the moving average case, and the two autoregressive cases. In other words, the normalizing factor differs in each of these three cases.Finally, a specific case of the functional central limit theorem in the spatial setting is stated and proved. The assumptions made here are placed on the autocovariance functions. We then discuss some specific examples and provide a test statistics based on the periodogram ordinate.
Title: Spatial Models with Specific Error Structures.
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Name(s): Adu, Nathaniel, Author
Richardson, Gary, Committee Chair
Mohapatra, Ram, Committee Member
Song, Zixia, Committee Member
Lang, Sheau-Dong, Committee Member
University of Central Florida, Degree Grantor
Type of Resource: text
Date Issued: 2019
Publisher: University of Central Florida
Language(s): English
Abstract/Description: The purpose of this dissertation is to study the first order autoregressive model in the spatial context with specific error structures. We begin by supposing that the error structure has a long memory in both the i and the j components. Whenever the model parameters alpha and beta equal one, the limiting distribution of the sequence of normalized Fourier coefficients of the spatial process is shown to be a function of a two parameter fractional Brownian sheet. This result is used to find the limiting distribution of the periodogram ordinate of the spatial process under the null hypothesis that alpha equals one and beta equals one. We then give the limiting distribution of the normalized Fourier coefficients of the spatial process for both a moving average and autoregressive error structure. Two cases of autoregressive errors are considered. The first error model is autoregressive in one component and the second is autoregressive in both components. We show that the normalizing factor needed to ensure convergence in distribution of the sequence of Fourier coefficients is different in the moving average case, and the two autoregressive cases. In other words, the normalizing factor differs in each of these three cases.Finally, a specific case of the functional central limit theorem in the spatial setting is stated and proved. The assumptions made here are placed on the autocovariance functions. We then discuss some specific examples and provide a test statistics based on the periodogram ordinate.
Identifier: CFE0007772 (IID), ucf:52385 (fedora)
Note(s): 2019-12-01
Ph.D.
Sciences,
Doctoral
This record was generated from author submitted information.
Subject(s): Autoregressive spatial process -- Moving average -- Unit roots -- Brownian sheet.
Persistent Link to This Record: http://purl.flvc.org/ucf/fd/CFE0007772
Restrictions on Access: campus 2020-12-15
Host Institution: UCF

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