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Inclusion and exclusion of data or parameters in the general linear model

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  • Jammalamadaka, S. Rao
  • Sengupta, D.

Abstract

This paper revisits the topic of how linear functions of observations having zero expectation, play an important role in our statistical understanding of the effect of addition or deletion of a set of observations in the general linear model. The effect of adding or dropping a group of parameters is also explained well in this manner. Several sets of update equations were derived by previous researchers in various special cases of the general set-up that we consider here. The results derived here bring out the common underlying principles of these update equations and help integrate these ideas. These results also provide further insights into recursive residuals, design of experiments, deletion diagnostics and selection of subset models.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:12:p:1235-1247
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    References listed on IDEAS

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    1. Nieto, Fabio H. & Guerrero, Victor M., 1995. "Kalman filter for singular and conditional state-space models when the system state and the observational error are correlated," Statistics & Probability Letters, Elsevier, vol. 22(4), pages 303-310, March.
    2. Pordzik, Pawe[does not divide] R., 1992. "Adjusting of estimates in general linear model with respect to linear restrictions," Statistics & Probability Letters, Elsevier, vol. 15(2), pages 125-130, September.
    3. 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.
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    Cited by:

    1. Bo Jiang & Yongge Tian, 2022. "Equivalence Analysis of Statistical Inference Results under True and Misspecified Multivariate Linear Models," Mathematics, MDPI, vol. 11(1), pages 1-16, December.
    2. Lu, Changli & Gan, Shengjun & Tian, Yongge, 2015. "Some remarks on general linear model with new regressors," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 16-24.

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