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Effective Methodologies for High-Dimensional Data(Special Topic:The JSS Research Prize Lecture)

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  • 日本統計学会研究業績賞受賞者特別寄稿論文 高次元データの統計的方法論
  • ニホン トウケイ ガッカイ ケンキュウ ギョウセキショウ ジュショウシャ トクベツ キコウ ロンブン コウジゲン データ ノ トウケイテキ ホウホウロン
  • 高次元データの統計的方法論(日本統計学会研究業績賞受賞者特別寄稿論文)
  • 日本統計学会研究業績賞受賞者特別寄稿論文 高次元データの統計的方法論
  • Effective Methodologies for High-Dimensional Data

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Abstract

In this paper, we consider statistical methodologies for high-dimensional data. We first clarify the limit of the conventional principal component analysis (PCA) for high-dimensional data. In order to overcome the curse of dimensionality, we introduce two effective PCAs called the noise-reduction methodology and the cross-data-matrix (CDM) methodology. We further introduce the extended CDM methodology, which offers an unbiased estimator having small asymptotic variance and low computational cost, for parameters appearing in high-dimensional data analysis. We give correlation tests and inference on multiclass mean vectors for high-dimensional data, and discuss sample size detemination to ensure prespecified high accuracy for inference. Finally, we provide two effective discriminant procedures: a distance-based classifier and a geometric classifier, which can ensure high accuracy in misclassification rates.

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