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July, 1976 When is a Sum of Squares an Analysis of Variance?
Arthur Albert
Ann. Statist. 4(4): 775-778 (July, 1976). DOI: 10.1214/aos/1176343550

Abstract

A sum of squares can be partitioned into sums of quadratic forms whose kernels are projections. If these projections are mutually orthogonal and add to the identity, then, under the classical fixed effects linear model, the terms of the decomposition are mutually independent and are distributed as multiples of chi-square. In this paper we exhibit necessary and sufficient conditions for a specified sum of squares decomposition to have this property in the case of the mixed model.

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Arthur Albert. "When is a Sum of Squares an Analysis of Variance?." Ann. Statist. 4 (4) 775 - 778, July, 1976. https://doi.org/10.1214/aos/1176343550

Information

Published: July, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0337.62052
MathSciNet: MR413379
Digital Object Identifier: 10.1214/aos/1176343550

Subjects:
Primary: 62J10
Secondary: 62E20

Keywords: Analysis of variance , Henderson's method , mixed model , projections , sums of squares , variance components

Rights: Copyright © 1976 Institute of Mathematical Statistics

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Vol.4 • No. 4 • July, 1976
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