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Selection of Predictors and Estimators in Spatial Statistics

Bradley, Jonathan R
http://rave.ohiolink.edu/etdc/view?acc_num=osu1374059401

Abstract Details

2013, Doctor of Philosophy, Ohio State University, Statistics.
There are many methods for prediction and estimation available in the spatial statistics literature. Predictors (and estimators) are often derived using different assumptions on the stochastic process, or they may be purely deterministic in nature. In this dissertation, we propose criteria to select from among a collection of competing spatial predictors, and from among a collection of competing estimators of the unknown and deterministic mean. This dissertation consists of an introductory chapter and three self-contained chapters. In the introductory chapter, we develop two types of selection criteria: criteria for estimator selection and criteria for predictor selection. In particular, we consider three different selection criteria problems for a spatial hierarchical statistical model in Chapters 2 through 4, respectively. In Chapter 2, we select from among a finite collection of competing spatial predictors of a hidden spatial process. The conventional approach for spatial-predictor selection is to use a criterion that estimates the average "performance" of each spatial predictor over the entire spatial domain. We call this approach global spatial-predictor selection, and the resulting chosen predictor a globally selected predictor (GSP). We consider selecting spatial predictors at each spatial location in the domain of interest based on its individual "performance," which we call local spatial-predictor selection. There might be regions of the spatial domain where different predictors are selected; the combination of these results is a spatial predictor we call a locally selected predictor (LSP). In Chapter 3, we propose criteria to select spatial basis functions for the Spatial Random Effects (SRE) model, which is a random linear combination of spatial basis functions. In this chapter, we introduce information criteria and an adaptive algorithm based on local information criteria to select the spatial basis functions. Then, in Chapter 4, we introduce a criterion to select estimators of the mean of a multivariate random vector. This chapter is the most general of all the chapters, since the criterion is derived for a general multivariate random-vector that is not necessarily defined on a spatial domain. The methodology proposed in this dissertation is supported using simulation experiments, and demonstrated using a dataset of global measurements of Carbon Dioxide, which were made available due to the Atmospheric InfraRed Sounder (AIRS) instrument on NASA's Aqua satellite.
Tao Shi (Advisor)
191 p.
Statistics
model selection; information criteria; spatial statistics; predictor averaging

Recommended Citations

Citations

  • Bradley, J. R. (2013). Selection of Predictors and Estimators in Spatial Statistics [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1374059401

    APA Style (7th edition)

  • Bradley, Jonathan. Selection of Predictors and Estimators in Spatial Statistics. 2013. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1374059401.

    MLA Style (8th edition)

  • Bradley, Jonathan. "Selection of Predictors and Estimators in Spatial Statistics." Doctoral dissertation, Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1374059401

    Chicago Manual of Style (17th edition)

osu1374059401
294
© 2013, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.