SPECTRAL ANALYSIS OF MULTIVARIATE BINARY DATA

抄録

A generalization of spectral (Fourier) analysis to the analysis of multivariate binary data is shown in this paper. The spectral analysis discussed here involves (1) identifying a group which retains the relevant statistical problem unchanged, (2) finding mutually orthogonal subspaces which are invariant under the action of the group, and (3) calculating the orthogonal projections of the data vector onto the invariant subspaces. Groups considered in this paper are Z^p₂ (p-fold product of the group of integers mod 2) and S_p (the symmetric group on p letters).
Group representation theory is extensively used in the development of the procedures, and hence it can be said that the background theory of the analysis is mathematical. However, the principle underlying the analysis is that of exploratory data analysis, and this will be shown in the practical examples in the paper. The present study is closely related to the analysis of variance (ANOVA) of 2^p-factorial design, loglinear models for 2^p-type contingency table, and the discriminant analysis for multivariate binary data.