A new confidence interval for all characteristic roots of a covariance matrix |
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Authors: | Fumitake Sakaori Takayuki Yamada Akihisa Kawamura Takakazu Sugiyama |
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Affiliation: | (1) College of Sociology, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima-ku, Tokyo 171-8501, Japan;(2) Department of Mathematics, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo, Japan |
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Abstract: | Confidence intervals for all of the characteristic roots of a sample covariance matrix are derived. Using a perturbation expansion, we obtain a new confidence interval for these roots. Then, we propose another confidence interval based on the results of Monte Carlo simulations. Since it is based on simulations, this new confidence interval is both narrower and more accurate than others when the difference between the largest and smallest characteristic roots of the population covariance matrix is large. |
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Keywords: | Characteristic root Confidence interval Perturbation expansion |
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