Regression on a Random Field

Abstract

The use of observations of a random function in space (random field) as independent variables in regression is considered including the numerical aspects. Details are presented for obtaining a numerical approximation to a Karhunen-Loève expansion when the random function is observed at a large number of points. The procedure involves a two stage modified principal component analysis. The dependent variable is then regressed on the principal components. An example from meteorology is presented. The random field is the 700 mb height surface observed at 505 points over the northern hemisphere. The dependent variable is the temperature at Washington, D. C. A by-product of the analysis is an estimate of the generalized spectrum and covariance function of the random field without assuming symmetry.