×

zbMATH — the first resource for mathematics

Updates of statistics in a general linear model: A statistical interpretation and applications. (English) Zbl 0825.62062
Summary: We consider a general linear model \((y,\mathbb{X} ,\Sigma)\) where \(\Sigma\) is a general positive definite matrix and \(\mathbb{X}\) is possibly rank- deficient. We give updated formulae for various statistical quantities of interest (BLUEs, residual sum of squares, etc.) in the following situations: introduction of an additional observation, deletion of an observation, inclusion of a new regressor and deletion of a regressor. We give the formulae in statistical terminology so that their significance is better understood. We then give an application of these results to regression diagnostics in the linear model with correlation errors.

MSC:
62-XX Statistics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DOI: 10.1002/0471725153 · doi:10.1002/0471725153
[2] Bhimasankaram P., to appear in Tamkang Journal of Mathematics (1993)
[3] Bhimasankaram, P., Sengupta, D. and Ramanathan, S. (1994). Recursive inference in a general linearmodel, to appear in Sankhya Ser. A
[4] Chatterjee S., Sensitivity Analysis in Linear Regression (1986)
[5] DOI: 10.2307/2684322 · doi:10.2307/2684322
[6] DOI: 10.1080/00949657308810051 · Zbl 0283.62062 · doi:10.1080/00949657308810051
[7] DOI: 10.1111/j.1467-842X.1985.tb00560.x · Zbl 0568.62064 · doi:10.1111/j.1467-842X.1985.tb00560.x
[8] DOI: 10.2307/2287520 · Zbl 0475.62052 · doi:10.2307/2287520
[9] Mcgillchrist C.A., Journal of the Royal Statistical Society 41 pp 65– (1979)
[10] Mitra S.K., Sankhya Ser. A 33 pp 396– (1971)
[11] Paige C.C., Communications in Statistics Ser. B 7 pp 437– (1978)
[12] Plackett R.L., Biometrika 37 pp 149– (1950)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.