ANOVA and the minimal least squares estimator

Oskar Maria Baksalary and Götz Trenkler

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 22, 7362-7370

Abstract: The one-way classification model of ANOVA (analysis of variance) is considered by exploiting an original approach based on a particular representation of the Moore–Penrose inverse of a columnwise partitioned matrix. By deriving various characteristics of the model, it is demonstrated that the utilized expression for the inverse is well-tailored to cope with the problem under consideration. One of the established results indicates that the solution to the normal equations in ANOVA customarily provided in the literature is not necessarily the minimal least squares solution.

Date: 2025
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DOI: 10.1080/03610926.2025.2474626

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