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Residuals for the linear model with general covariance structure

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  • John Haslett
  • Kevin Hayes

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.

Suggested Citation

  • John Haslett & Kevin Hayes, 1998. "Residuals for the linear model with general covariance structure," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(1), pages 201-215.
    • Handle: RePEc:bla:jorssb:v:60:y:1998:i:1:p:201-215
    DOI: 10.1111/1467-9868.00119
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    Cited by:

    1. Shi, Lei & Chen, Gemai, 2012. "Deletion, replacement and mean-shift for diagnostics in linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 202-208, January.
    2. Li, Zaixing & Xu, Wangli & Zhu, Lixing, 2009. "Influence diagnostics and outlier tests for varying coefficient mixed models," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2002-2017, October.
    3. Andrea Cerioli & Marco Riani, 2002. "Robust methods for the analysis of spatially autocorrelated data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 11(3), pages 335-358, October.
    4. J. Haslett & M. Whiley & S. Bhattacharya & M. Salter‐Townshend & Simon P. Wilson & J. R. M. Allen & B. Huntley & F. J. G. Mitchell, 2006. "Bayesian palaeoclimate reconstruction," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 169(3), pages 395-438, July.
    5. Tommaso Proietti, 2003. "Leave‐K‐Out Diagnostics In State‐Space Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(2), pages 221-236, March.
    6. Xiaowen Dai & Libin Jin & Anqi Shi & Lei Shi, 2016. "Outlier detection and accommodation in general spatial models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(3), pages 453-475, August.
    7. Grzegorz Trzmiel & Jaroslaw Jajczyk & Ewa Kardas-Cinal & Norbert Chamier-Gliszczynski & Waldemar Wozniak & Konrad Lewczuk, 2021. "The Condition of Photovoltaic Modules under Random Operation Parameters," Energies, MDPI, vol. 14(24), pages 1-18, December.
    8. Sánchez, Ismael, 2001. "New in-sample prediction errors in time series with applications," DES - Working Papers. Statistics and Econometrics. WS ws011107, Universidad Carlos III de Madrid. Departamento de Estadística.

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