On Fixed Effects Estimation for Spatial Regression Under the Presence of Spatial Confounding

Yung-Huei Chiou

Department of Mathematics

National Changhua University of Education

S0322011@gm.ncue.edu.tw

    Spatial regression models are often used to analyze the ecological and environmental data sets over a continuous spatial support. Issues of collinearity among covariates are often considered in modeling, but only rarely in discussing the relationship between covariates and unobserved spatial random processes. Past researches have shown that ignoring this relationship (or, spatial confounding) would have significant influences on the estimation of regression parameters. To improve this problem, an idea of restricted spatial regression is used to ensure that the unobserved spatial random process is orthogonal to covariates, but the related inferences are mainly based on Bayesian frameworks. In this thesis, an adjusted generalized least squares estimation method is proposed to estimate regression coefficients, resulting in the estimators that perform better than the conventional methods. Under the frequentist framework, statistical inferences of the proposed methodology are justified both in theories and via simulation studies. Finally, an application of a water acidity data set in the Blue Ridge region of the eastern U.S. is analyzed for illustration. This is a joint work with Hong-Ding Yang and Chun-Shu Chen.

Keyword: Bias, Generalized least squares, Maximum likelihood estimate, Random effects, Restricted spatial regression