Linear regression with spatially correlated data.

Abstract

In this dissertation, the analysis of spatial data through regression is investigated. Multiple observations taken from sites are assumed to be spatially dependent. Our linear model includes a pure error and a spatial error term whose covariance structure is given by an unknown linear combination of 2 known covariograms. The pure and spatial error terms also have separate scale parameters. Our first concern is with the estimation of the parameters of this model. An algorithm to estimate these parameters is proposed as well as a consistent estimator for one of the spatial parameters. Numerical simulations support the use of our algorithm. The second main issue is that of asymptotics. To that end, a formula for the inverse of the variance-covariance matrix of observations is developed. Limits of the asymptotic variance of the parameter estimates as the number of observations per site increases are found with this formula. On the other hand, specific sampling schemes are studied when considering the asymptotics for the number of sites going to infinity. From the simulation and asymptotic results, some rules for experimental design are given. Extensions to more general models are made and areas of future research including possible applications are suggested.