Spatial Regression Using Kernel-Averaged Predictors

• Activity Number: 461
• Type: Topic Contributed
• Date/Time: Wednesday, August 4, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Matthew Joseph Heaton*+ and Alan E. Gelfand
• Companies: Duke University and Duke University
• Keywords: spatial linear model ; kernel smoothing ; block averaging ; Gaussian process

Abstract

Traditional spatial linear regression models assume the mean of the response is a linear combination of predictors measured at the same location as the response. In spatial applications, however, it seems plausible that neighboring predictors can also inform about the response. This article proposes using unobserved kernel averaged predictors in such regressions. The kernels are parametric introducing additional parameters that are estimated with the data. Properties and challenges of using kernel averaged predictors within a regression model are detailed in the simple case of a univariate response and a single predictor. Additionally, extensions to multiple predictors and generalized linear models are discussed. The methods are demonstrated using a data set of dew duration and shrub density.