B1141
Title: Dimension reduction for spatial regression: The spatial predictor envelope
Authors: Hossein Moradi Rekabdarkolaee - South Dakota State University (United States) [presenting]
Abstract: Natural sciences such as geology and forestry often utilize regression models for spatial data with high-dimensional predictors and moderate sample sizes. In this case, efficient estimation of the regression parameters is crucial for both model interpretation and prediction. The predictor envelope is a method of dimension reduction for linear regression with multivariate predictors that assumes certain linear combinations of the predictors are immaterial to the regression. The method can result in substantial gains in estimation efficiency and prediction accuracy over traditional maximum likelihood and least squares estimates. While predictor envelopes have been developed and studied for independent data, no work has been done adapting predictor envelopes to spatial data. The predictor envelope is adapted to a popular spatial model to form the spatial predictor envelope. Maximum likelihood estimates for the SPE are derived, along with asymptotic distributions for the estimates given certain assumptions, showing the SPE estimates to be asymptotically more efficient than generalized least squares, the typical spatial regression estimates. Further, we study the SPE in the context of spatial prediction, or universal kriging, discussing the contexts in which the SPE can provide gains over the typical universal kriging predictions. The effectiveness of the proposed model is illustrated through simulation studies and real data analysis.
