Variance Estimation in Spatial Regression Using a Nonparametric Semivariogram Based on Residuals

The empirical semivariogram of residuals from a regression model with stationary errors may be used to estimate the covariance structure of the underlying process. For prediction (kriging) the bias of the semivariogram estimate induced by using residuals instead of errors has only a minor eeect because the bias is small for small lags. However, for estimating the variance of estimated regression coeecients and of predictions, the bias due to using residuals can be quite substantial. Thus we propose a method for reducing this bias. The adjusted empirical semi-variogram is then isotonized and made conditionally negative-deenite and used to estimate the variance of estimated regression coeecients in a general estimating equations setup. Simulation results for least squares and robust regression show that the proposed method works well in linear models with stationary correlated errors.