Numerical Computation for the Eigenvalue Distributions of a Wishart Matrix

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  • ウィシャート行列の固有値分布とその数値計算
  • 日本統計学会賞受賞者特別寄稿論文 ウィシャート行列の固有値分布とその数値計算
  • ニホン トウケイ ガッカイショウ ジュショウシャ トクベツ キコウ ロンブン ウィシャート ギョウレツ ノ コユウチ ブンプ ト ソノ スウチ ケイサン

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Wishart matrix is one of typical random matrices and a constant times of a sample covariance matrix. The larger eigenvalues and corresponding eigenvectors of the sample covariance matrix are important to assess results from a sample in multivariate statistical analysis. On the other hand, the smaller ones are related to collinearity in a regression model. This paper discusses numerical computation for the istributions of the eigenvalues and the largest eigenvector for a Wishart matrix, and also show that approximations based on normal and chi-square distributions have high accuracy.

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