Date of Graduation
Spatial data analysis (SDA) has become an essential part of the researcher's toolbox in regional economics, environmental economics, resource economics and other fields where space matters. Quantitative methods of SDA have their roots in linear algebra, statistics, computational geometry, etc. However, generic methods are not well adopted for the specifics of SDA, which may result in their poor computational performance when applied to spatial data. This dissertation consists of two essays, which deal with two contemporary computational issues of SDA: (1) Computational and algorithmic issues in the evaluation of the likelihood function for regression models with spatial dependence. (2) On constructing a spatial weights matrix. In each of the essays a major area of concentration is a specific problem of SDA. The essays contain a review of theoretical and analytical results on the matter as well as a discussion of the practical issues associated with the use of currently available solutions. The major component of the essays is to emphasize the introduction and analysis of new approaches for solving these problems. Theoretical analysis is conducted in terms of asymptotic properties of the methods and their computational parameters (robustness, stability and the accuracy of the results). The main contribution of the first essay is the development of two methods (one is based on use of characteristic polynomials and another on the use of traces of powered matrices) to compute the log-Jacobian of a large sparse matrix. The main contribution of the second essay is the introduction of two methods based on the plane sweep algorithm to construct a distance based spatial weights matrix. The analysis of the new methods indicates that their computational parameters are superior to existing techniques. The implementation issues associated with the use of the proposed methods are also part of the discussion, and complete code of C/C++ programs is given in the Appendices. Finally, the essays contain the results of the empirical experiments obtained with a number of data sets. These results support the conclusion that the newly developed methods are viable techniques designed for solving large scale problems and are the fastest methods.
Smirnov, Oleg, "Computational aspects of spatial data analysis." (1998). Graduate Theses, Dissertations, and Problem Reports. 9789.