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Residuals for the linear model with general covariance structure
Authors:John Haslett  & Kevin Hayes
Institution:Trinity College Dublin, Republic of Ireland,;University of Limerick, Republic of Ireland
Abstract:A general theory is presented for residuals from the general linear model with correlated errors. It is demonstrated that there are two fundamental types of residual associated with this model, referred to here as the marginal and the conditional residual. These measure respectively the distance to the global aspects of the model as represented by the expected value and the local aspects as represented by the conditional expected value. These residuals may be multivariate. Some important dualities are developed which have simple implications for diagnostics. The results are illustrated by reference to model diagnostics in time series and in classical multivariate analysis with independent cases.
Keywords:Cross-validation  Diagnostics  Generalized least squares  Geostatistics  Kriging  Mahalanobis distance  Residuals  Time series
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