Mahalanobis Distance and General Linear Hypotheses in Linear Models

Paul Janssen (), Luc Duchateau () and Noël Veraverbeke ()
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Paul Janssen: Center for Statistics, Data Science Institute, Hasselt University
Luc Duchateau: Ghent University, Biometrics Research Group
Noël Veraverbeke: Center for Statistics, Data Science Institute, Hasselt University

Chapter Chapter 15 in Asymptotic and Methodological Statistics, 2026, pp 297-315 from Springer

Abstract: Abstract This contribution is an educational plea to put the Mahalanobis distance ( $$d_M$$ d M ) more in the spotlight when teaching linear models. When compared to statistical multivariate analysis, we learn that the role of the Mahalanobis distance in inference for linear models is underrated. The Mahalanobis distance is in fact the key ingredient to arrive at confidence ellipsoids and F-tests for estimable parameters. We therefore want to stress, in this educational note, the usefulness and the obviousness of the Mahalanobis distance in linear models (regression models and multi-factor models), by showing the role of the Mahalanobis distance not only in regression diagnostics but also—even more importantly—in testing general linear hypotheses. Although the results in this note are not intrinsically new, the didactic message is that the Mahalanobis distance provides an overarching way to treat statistical hypotheses testing in linear models in a unified way. We will in fact demonstrate that testing is (knowing basic matrix algebra) easy to explain and to teach when looking at it from a Mahalanobis distance perspective.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-032-07178-1_15

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DOI: 10.1007/978-3-032-07178-1_15

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