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A Simple Derivation of Deletion Diagnostic Results for the General Linear Model with Correlated Errors

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  • John Haslett

Abstract

A general, simple and intuitive derivation is provided for diagnostics associated with the deletion of arbitrary subsets for the linear model with general covariance structure. These are seen to be most simply expressed, even for the well‐studied case of independent and identically distributed data, in terms of a residual known variously as the conditional residual, the deletion prediction residual and the cross‐validation residual. Particularly simple specializations arise when the subsets are of size 1 and of size 2, but the method is easy to apply for all subsets and to conditional deletions.

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  • John Haslett, 1999. "A Simple Derivation of Deletion Diagnostic Results for the General Linear Model with Correlated Errors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 603-609.
    • Handle: RePEc:bla:jorssb:v:61:y:1999:i:3:p:603-609
    DOI: 10.1111/1467-9868.00195
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    Cited by:

    1. Shi, Lei & Chen, Gemai, 2008. "Case deletion diagnostics in multilevel models," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 1860-1877, October.
    2. 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.
    3. 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.
    4. Gumedze, Freedom N. & Welham, Sue J. & Gogel, Beverley J. & Thompson, Robin, 2010. "A variance shift model for detection of outliers in the linear mixed model," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2128-2144, September.
    5. Shi, Lei & Lu, Jun & Zhao, Jianhua & Chen, Gemai, 2016. "Case deletion diagnostics for GMM estimation," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 176-191.
    6. Jammalamadaka, S. Rao & Sengupta, D., 2007. "Inclusion and exclusion of data or parameters in the general linear model," Statistics & Probability Letters, Elsevier, vol. 77(12), pages 1235-1247, July.
    7. 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.
    8. Brian J. Reich & James S. Hodges & Vesna Zadnik, 2006. "Effects of Residual Smoothing on the Posterior of the Fixed Effects in Disease-Mapping Models," Biometrics, The International Biometric Society, vol. 62(4), pages 1197-1206, December.
    9. 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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