Spatially varying coefficient models: Theory and methods

dc.contributor.advisor Lily Wang Mu, Jingru
dc.contributor.department Statistics 2019-11-04T21:54:23.000 2020-06-30T03:19:00Z 2020-06-30T03:19:00Z Thu Aug 01 00:00:00 UTC 2019 2020-07-18 2019-01-01
dc.description.abstract <p>This thesis contains three papers focusing on estimation and inference in the spatial data. In the first paper (Chapter 2), we study the estimation and inference in spatial varying coefficient models for data distributed over complex domains. We use bivariate splines over triangulations to represent the coefficient functions. The estimators of the coefficient functions are consistent, and rates of convergence of the proposed estimators are established.</p> <p>In the second paper (Chapter 3), we extend the idea from the first project and consider a class of flexible partially linear spatially varying coefficient autoregressive models. Under some regularity conditions, the estimated constant coefficients are asymptotically normally distributed, and the estimated varying coefficients are consistent and possess the optimal convergence rate. We further develop an efficient algorithm to calculate the distance between neighbors over complex domains. In addition, we propose a model selection approach to identify explanatory variables with constant and varying effects. The proposed method is much more computationally efficient than the local smoothing method such as the geographically weighted regression, and thus capable of handling large scale of spatial data. The performance of the proposed estimation and model identification methods are evaluated by two simulation examples and the Sydney real estate dataseet.</p> <p>Note that selecting the smoothing parameter and triangulation mesh is a critical part of im- plementing the bivariate penalized spline fitting in the first paper and second paper. In the third paper (Chapter 4), we propose using the generalized cross-validation to show how to select the roughness penalty parameter and the triangulation jointly. We demonstrate the effectiveness of the proposed method via extensive numerical studies. We extend our method to spatially varying coefficient models, a generalization of linear regression models for exploring non-stationarity of a regression relationship in spatial data analysis.</p>
dc.format.mimetype application/pdf
dc.identifier archive/
dc.identifier.articleid 8526
dc.identifier.contextkey 15681555
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath etd/17519
dc.language.iso en
dc.source.bitstream archive/|||Fri Jan 14 21:24:56 UTC 2022
dc.subject.disciplines Statistics and Probability
dc.subject.keywords bivariate splines
dc.subject.keywords penalized splines
dc.subject.keywords spatial data
dc.subject.keywords triangulation
dc.subject.keywords varying coefficient models
dc.title Spatially varying coefficient models: Theory and methods
dc.type article
dc.type.genre dissertation
dspace.entity.type Publication
relation.isOrgUnitOfPublication 264904d9-9e66-4169-8e11-034e537ddbca Statistics dissertation Doctor of Philosophy
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