- Title
- Approximate profile likelihood estimation for spatial-dependence parameters
- Author
- Li, Hongfei
- Degree
- Doctor of Philosophy, Ohio State University,
Statistics, 2007.
- Advisor
- Catherine A. Calder
- Abstract
- The problem of accounting for spatial dependence in statistical analyses has received considerable attention due to the prevalence of spatial data in many disciplines. Typically, statistical analyses proceed by first testing if there is spatial dependence in the data. Then, if we find it, we want to measure its strength. Previous studies either do not provide obvious estimators of spatial-dependence parameters in commonly used models, or they cannot be expressed in closed form. For example, maximum likelihood estimators (MLEs) cannot typically be expressed in closed form. In this dissertation, we develop alternative closed-form measures of spatial dependence, which we call APLEs, as they are approximate profile likelihood estimators of parameters in spatial lattice models. While we consider three commonly used spatial lattice models, this dissertation primarily focuses on the APLEs for the simultaneous autoregressive (SAR) model. For this model, we derive APLEs under different scenarios where the nuisance parameters are known or unknown. We include both theoretical and simulation-based motivation (including comparison to the MLE) for using APLE as an estimator, and we explore its asymptotic properties. In conjunction, we propose the APLE scatterplot and local APLEs for assessing the strength of spatial dependence visually and for identifying “spatial outliers”. Crime data from Columbus, Ohio are used to illustrate the use of our APLE statistics in exploratory data analyses. In addition to considering the properties of APLE as an estimator of spatial dependence, we show that APLE can be used as a test statistic. Finally, we derive APLEs in the presence of measurement error, as well as heteroskedasticity. Beyond the SAR-based APLE, we also derive APLEs for spatial-dependence parameters in the conditional autoregressive (CAR) and spatial moving-average (SMA) models. To accommodate features of these models, the APLE approach must be modified slightly. The efficiency of the APLEs for these two lattice models is evaluated, and heteroskedasticity extensions are provided.
- Subject Headings
- Statistics
Document number: osu1191267954.
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