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On a statistic useful in dimensionality reduction in multivariable linear stochastic system |
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| Authors: | T Sugiyama H Tong |
| Institution: | 1. The Institute of Statistical Mathematics , Tokyo, Japan;2. Institute of Science and Technology , The University of Manchester , England |
| Abstract: | 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. |
| Keywords: | linear multivariable stochastic control system principal component analysis dimensionality reduction ratios of sample eigenvalues sugiura’s expansion approximate distribution of ratio statistic |