Array Variate Random Variables with Multiway Kro- necker Delta Covariance Matrix Structure

Abstract

Standard statistical methods applied to matrix random variables often fail to describethe underlying structure in multiway data sets. After a review of the essential background material,this paper introduces the notion of array variate random variable. A normal array variate randomvariable is dened and a method for estimating the parameters of array variate normal distributionis given. We introduce a technique called slicing for estimating the covariance matrix of highdimensional data. Finally, principal component analysis and classication techniques are developedfor array variate observations and high dimensional data.