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- Title
Variance Estimation in Spatial Regression Using a Non-parametric Semivariogram Based on Residuals.
- Authors
Kim, Hyon-Jung; Boos, Dennis D.
- Abstract
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 effect because the bias is small for small lags. However, for estimating the variance of estimated regression coefficients 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 semivariogram is then isotonized and made conditionally negative-definite and used to estimate the variance of estimated regression coefficients 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.
- Subjects
ANALYSIS of variance; ESTIMATION theory; NONPARAMETRIC statistics; REGRESSION analysis; MATHEMATICAL statistics; PREDICTION theory
- Publication
Scandinavian Journal of Statistics, 2004, Vol 31, Issue 3, p387
- ISSN
0303-6898
- Publication type
Article
- DOI
10.1111/j.1467-9469.2004.02-025.x