On a statistic useful in dimensionality reduction in multivariable linear stochastic system
T. Sugiyama, Howell Tong · Communication in Statistics- Theory and Methods · 1976
In this paper we study the sampling properties of a test statistic which has important applications in the area of linear stochastic control systems with multi-inputs and multi-outputs. The statistic is the ratio of a partial sum of the eigenvalues of a sample covariance matrix and its trace. It turns out that using a method due to Sugiura we may derive a useful approximation for its distribution up to and including terms of order l/n, where n denotes the appropriate size. Numerical illustrations using real data are given.