Interpolation and optimal linear prediction

This paper is concerned with the interpolation of spatially distributed observations of a quantitative phenomenon, sometimes referred to as kriging. This activity can be understood as a prediction procedure for values of random functions under stationarity assumptions in a polynomial linear regression context. After a heuristic and an exact derivation of the best linear unbiased prediction procedure (and the variance of prediction error) if the covariance function relating covariance between two possible observations to their mutual distance is known, follows the introduction of weaker assumptions admitting the definition of the variance only for increments of a certain order by a pseudoco–variance function. A particular related case is the so–called semivariogram for increments of order one. The prediction procedure turns out to be similar to that in the previous situation. The weaker assumptions allow an unbiased estimation of the unknown pseudocovahance function of polynomial form under restrictions imposed by Fourier transformation. Extension from point–wise observations or predictions to area or volume averages is touched upon.     

Analysis of Spatial Autocorrelation in House Prices

This article examines spatial autocorrelation in transaction prices of single-family properties in Dallas, Texas. The empirical analysis is conducted using a semilog hedonic house price equation and a spherical autocorrelation function with data for over 5000 transactions of homes sold between 1991:4 and 1993:1. Properties are geocoded and assigned to separate housing submarkets within metropolitan Dallas. Hedonic and spherical autocorrelation parameters are estimated separately for each submarket using estimated generalized least squares (EGLS). We find strong evidence of spatial autocorrelation in transaction prices within submarkets. Results for spatially autocorrelated residuals are mixed. In four of eight submarkets, there is evidence of spatial autocorrelation in the hedonic residuals for single-family properties located within a 1200 meter radius. In two submarkets, the hedonic residuals are spatially autocorrelated throughout the submarket, while the hedonic residuals are spatially uncorrelated in the remaining two submarkets. Finally, we compare OLS and kriged EGLS predicted values for properties sold during 1993:1. Kriged EGLS predictions are more accurate than OLS in six of eight submarkets, while OLS has smaller prediction errors in submarkets where the residuals are spatially uncorrelated and the estimated semivariogram has a large variance.