Spectral PCA for MANOVA and data over binary trees

Abstract We extend a concept of ANOVA broader than the traditional variance component models to MANOVA. Within this framework we can derive a spectral principal component analysis (PCA) and see how it generalises the same notion for weakly stationary vector time series. We then attempt to obtain analogous results for arrays of random variables over (i.e., indexed by the nodes of) binary trees, with only partial success. While there is an analogue of ANOVA and MANOVA for binary trees, the existence of spectral PCA there is unresolved.