Array variate random variables with multiway Kronecker delta covariance matrix structure

Standard statistical methods applied to matrix random variables often fail to describe the under lying 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 random variable is defined and amethod for estimating the parameters of array variate normal distribution is given. We introduce a technique called slicing for estimating the covariance matrix of high dimensional data. Finally, principal component analysis and classification techniques are developed for array variate observations and high dimensional data.

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