Fisher information matrix: A tool for dimension reduction, projection pursuit, independent component analysis, and more

Abstract

AbstractHui & Lindsay (2010) proposed a new dimension reduction method for multivariate data. It was based on the so‐called white noise matrices derived from the Fisher information matrix. Their theory and empirical studies demonstrated that this method can detect interesting features from high‐dimensional data even with a moderate sample size. The theoretical emphasis in that paper was the detection of non‐normal projections. In this paper we show how to decompose the information matrix into non‐negative definite information terms in a manner akin to a matrix analysis of variance. Appropriate information matrices will be identified for diagnostics for such important modern modelling techniques as independent component models, Markov dependence models, and spherical symmetry. The Canadian Journal of Statistics 40: 712–730; 2012 © 2012 Statistical Society of Canada