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Estimation of Bivariate Spatial Data

Onnen, Nathaniel J
http://rave.ohiolink.edu/etdc/view?acc_num=osu1616243660473062

Abstract Details

2021, Doctor of Philosophy, Ohio State University, Statistics.
Bivariate spatial models are used to represent the joint relationship between two processes observed over space. By modeling two processes jointly, we may be able to enhance parameter estimation and prediction over estimating the processes marginally. This dissertation will focus on statistical methods for bivariate geostatistical processes observed continuously in space, and bivariate areal processes observed on a countable partition of space. We will focus on a special class of bivariate geostatistical processes, the bivariate Mat\'ern process. Bivariate Mat\'ern processes are an attractive model due to their modeling flexibility over other bivariate process models like the Linear Model of Coregionalization (LMC). We investigate maximum likelihood (ML) estimates for the parameters of the bivariate Mat\'ern process. Computational procedures for ML estimates in the literature do not often constrain the processes to be positive definite. Also, little is known about the asymptotic properties of these ML estimators. Hence, we develop a procedure for computing ML estimates that preserves the positive definite covariance structure, and conduct a large-scale simulation study to explore the asymptotic properties of these ML estimates. We use the theory of ML estimation for univariate Mat\'ern processes to postulate what is estimable from the cross covariance function when the marginal process parameters are assumed known. We show that while the individual cross covariance parameters are not necessarily consistently estimable, a function of them may be, and may have root-$n$ convergence. We then use our ML estimation procedures to model and predict a bivariate spatial data set of daily temperatures and wind speeds in the eastern United States. In the context of modeling bivariate areal processes, we investigate generalized estimating equation approaches for modeling univariate and bivariate counts over regions in the presence of overdispersion. For scientific problems in which the inference of covariate effects are of interest, we investigate sandwich estimators to account for residual spatial dependence and cross dependence in the data. We motivate this work by developing spatial models to model the number of tobacco retailers across census tracts in the state of Ohio. These models are used to estimate the impact on socioeconomic and demographic characteristics by implementing licensing law strategies in order to reduce existing disparities.
Peter Craigmile (Advisor)
Oksana Chkrebtii (Committee Member)
Matthew Pratola (Committee Member)
Megan Roberts (Committee Member)
201 p.
Statistics
Spatial Statistics; Geostatistical Processes; Maximum Likelihood Estimation; Matern Covariance; Generalized Estimating Equations

Recommended Citations

Citations

  • Onnen, N. J. (2021). Estimation of Bivariate Spatial Data [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1616243660473062

    APA Style (7th edition)

  • Onnen, Nathaniel. Estimation of Bivariate Spatial Data. 2021. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1616243660473062.

    MLA Style (8th edition)

  • Onnen, Nathaniel. "Estimation of Bivariate Spatial Data." Doctoral dissertation, Ohio State University, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=osu1616243660473062

    Chicago Manual of Style (17th edition)

osu1616243660473062
181
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This open access ETD is published by The Ohio State University and OhioLINK.