8 research outputs found
On ANOVA-Like Matrix Decompositions
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