Award Date

12-15-2018

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematical Sciences

First Committee Member

Petros Hadjicostas

Second Committee Member

Hokwon A. Cho

Third Committee Member

Kaushik Ghosh

Fourth Committee Member

Ashok K. Singh

Number of Pages

78

Abstract

In this thesis, we study one of Ord's (1975) global spatial regression models.

Ord considered spatial regressive-autoregressive models to describe the interaction

between location and a response variable in the presence of several covariates. He also

developed a practical estimation method for the parameters of this regression model

using the eigenvalues of a weight matrix that captures the contiguity of locations.

We review the theoretical aspects of his estimation method and implement it in the

statistical package R.

We also implement Ord's methods on the Columbus, Ohio, crime data set from the

year 1980, which involves the crime rate of each neighborhood of the city as a response

variable and the average income and average house value of each neighborhood as

covariates. We use different weight matrices that capture different "nearest neighbor"

notions and compare the results.

Keywords

autoregressive; Columbus Ohio data; lattice structure; Ord's eigenvalue; spatial data; spatial parameter estimation

Disciplines

Applied Mathematics | Statistics and Probability

Language

English


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