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Residuals for the linear model with general covariance structure
Author(s) -
Haslett John,
Hayes Kevin
Publication year - 1998
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00119
Subject(s) - multivariate statistics , covariance , residual , mathematics , econometrics , general linear model , statistics , linear model , series (stratigraphy) , measure (data warehouse) , simple (philosophy) , conditional expectation , studentized residual , value (mathematics) , computer science , algorithm , data mining , paleontology , philosophy , epistemology , biology
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.