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June, 1964 Pseudo-Inverses in the Analysis of Variance
Peter W. M. John
Ann. Math. Statist. 35(2): 895-896 (June, 1964). DOI: 10.1214/aoms/1177703596


The normal equations in the analysis of variance with suitable side conditions give a unique set of estimates, $\tilde\beta_i$, of the parameters $\beta_i$. These estimates are unique linear forms in the actual observations. In the solutions to the normal equations they appear as linear forms in the treatment and block totals; these totals are not independent and so the forms in them are not unique. Thus the normal equations, while giving a unique solution vector, admit an infinite number of pseudo-inverses of the matrix $X' X$. In this paper the relationship between the two most common pseudo-inverses is discussed.


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Peter W. M. John. "Pseudo-Inverses in the Analysis of Variance." Ann. Math. Statist. 35 (2) 895 - 896, June, 1964.


Published: June, 1964
First available in Project Euclid: 27 April 2007

zbMATH: 0123.36705
MathSciNet: MR162315
Digital Object Identifier: 10.1214/aoms/1177703596

Rights: Copyright © 1964 Institute of Mathematical Statistics

Vol.35 • No. 2 • June, 1964
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