Application of Resampling Methods to the Choice of Dimension in Principal Component Analysis

作者: Ph. Besse , A. de Falguerolles

DOI: 10.1007/978-3-642-52468-4_11

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摘要: This paper investigates the problem of choice dimension in Principal Component Analysis (PCA). PCA is introduced as a model; loss function assessing stability fit considered. The then amounts to minimisation an expected which has be estimated. achieved by resampling methods. Different bootstrap and jackknife estimates are presented. behaviour these investigated on artificial data real data. resulting choices confronted with those given naive rules.

参考文章(13)
Bradley Efron, Jackknife‐After‐Bootstrap Standard Errors and Influence Functions Journal of the royal statistical society series b-methodological. ,vol. 54, pp. 83- 111 ,(1992) , 10.1111/J.2517-6161.1992.TB01866.X
P.H. Besse, H. Caussinus, L. Ferre, J. Fine, Principal components analysis and optimization of graphical displays Statistics. ,vol. 19, pp. 301- 312 ,(1988) , 10.1080/02331888808802103
Philippe Besse, PCA stability and choice of dimensionality Statistics & Probability Letters. ,vol. 13, pp. 405- 410 ,(1992) , 10.1016/0167-7152(92)90115-L
Rudolf Beran, Muni S. Srivastava, Bootstrap Tests and Confidence Regions for Functions of a Covariance Matrix Annals of Statistics. ,vol. 13, pp. 95- 115 ,(1985) , 10.1214/AOS/1176346579
Gary C. McDonald, Richard C. Schwing, Instabilities of Regression Estimates Relating Air Pollution to Mortality Technometrics. ,vol. 15, pp. 463- 481 ,(1973) , 10.1080/00401706.1973.10489073
J.J. Daudin, C. Duby, P. Trecourt, Stability of principal component analysis studied by the bootstrap method Statistics. ,vol. 19, pp. 241- 258 ,(1988) , 10.1080/02331888808802095
J.J. Daudin, C. Duby, P. Trécourt, Pca stability studied by the bootstrap and the infinitesimal jackknife method Statistics. ,vol. 20, pp. 255- 270 ,(1989) , 10.1080/02331888908802168
Richard A. Becker, John M. Chambers, Allan R. Wilks, The New S Language New S Language: A Programming Environment for Data Analysis and Graphics 1st. pp. 702- 702 ,(1988) , 10.1201/9781351074988