Spatial regression with spatial confounding is an important issue in statistical modeling, because it will lead to biased estimators of regression coefficients and inaccurate spatial predictors. This issue has received much attention in spatial statistics, but foundational questions of how to modify the biases of coefficient estimators in the presence of spatial confounding have not been adequately addressed under the frequentist framework. In this proposal, we attempt to propose a semiparametric method to estimate regression coefficients based on a fixed rank kriging technique. The idea does not require specifying a parametric covariance structure and hence is more flexible in modeling spatial covariance functions. In our proposal, a class of basis functions exacted from thin-plate splines is used, where the number of basis functions is expected to impact the resolution of the spatial random process and the estimation of regression coefficients. We will develop two aspects to select the number of basis functions which are designed toward two different inferences when the main goals lie respectively in the estimation of regression coefficients and spatial prediction. As a result, two estimators of regression coefficients and the consequent spatial predictors will be established. The proposed methodology can be applied to stationary or nonstationary spatial processes and it also can be applied to massive datasets without handling the computational issue of high-dimensional inverse matrices. Further, a variable selection criterion under the presence of spatial confounding will be discussed as well. Statistical inferences associated with the proposed methodology will be justified in theories and via simulation studies. Finally, a real data example will be analyzed for illustration.
|Effective start/end date
|1/08/19 → 31/07/20
UN Sustainable Development Goals
In 2015, UN member states agreed to 17 global Sustainable Development Goals (SDGs) to end poverty, protect the planet and ensure prosperity for all. This project contributes towards the following SDG(s):
- Fixed rank kriging
- high-dimensional covariance matrix
- mean squared error
- spatial confounding effects
- thin-plate splines
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