The analysis of variance plays a fundamental role in statistical theory and practice, the standard Euclidean geometric form being particularly well-established. The geometry and associated linear algebra underlying such standard analysis of variance methods permit, essentially direct, generalisation to other settings. Specifically, as jointly developed here: (a) to minimum distance estimation problems associated with subsets of pairwise orthogonal subspaces; (b) to matrix, rather than vector, contexts; and (c) to general, not just standard Euclidean, inner products, and their induced distance functions. To this end, we characterise inner products rendering pairwise orthogonal a given set of nontrivial subspaces of a linear space any two of which meet only at the origin. Applications in a variety of areas are highlighted, including: (i) the analysis of asymmetry, and (ii) asymptotic comparisons in Invariant Coordinate Selection and Independent Component Analysis. A variety of possible further generalisations and applications are noted.

Bove, G., Critchley, F., Sabolova, R., Van Bever, G. (2015). On ANOVA-Like Matrix Decompositions. In K. Nordhausen (a cura di), Modern Nonparametric, Robust and Multivariate Methods (pp. 425-440). Heidelberg : Springer [10.1007/978-3-319-22404-6_23].

On ANOVA-Like Matrix Decompositions

BOVE, Giuseppe
;
2015

Abstract

The analysis of variance plays a fundamental role in statistical theory and practice, the standard Euclidean geometric form being particularly well-established. The geometry and associated linear algebra underlying such standard analysis of variance methods permit, essentially direct, generalisation to other settings. Specifically, as jointly developed here: (a) to minimum distance estimation problems associated with subsets of pairwise orthogonal subspaces; (b) to matrix, rather than vector, contexts; and (c) to general, not just standard Euclidean, inner products, and their induced distance functions. To this end, we characterise inner products rendering pairwise orthogonal a given set of nontrivial subspaces of a linear space any two of which meet only at the origin. Applications in a variety of areas are highlighted, including: (i) the analysis of asymmetry, and (ii) asymptotic comparisons in Invariant Coordinate Selection and Independent Component Analysis. A variety of possible further generalisations and applications are noted.
978-3-319-22403-9
Bove, G., Critchley, F., Sabolova, R., Van Bever, G. (2015). On ANOVA-Like Matrix Decompositions. In K. Nordhausen (a cura di), Modern Nonparametric, Robust and Multivariate Methods (pp. 425-440). Heidelberg : Springer [10.1007/978-3-319-22404-6_23].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11590/282425
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