Diagnostics in Multivariate Data Analysis: Sensitivity Analysis for Principal Components and Canonical Correlations
Sensitivity analysis procedures are formulated for principal component and canonical correlation analyses based on Cook’s local influence (Cook, 1986). The relationships are discussed between the results of the procedures based on the local influence and those based on the influence functions. A numerical example is shown to illustrate the procedure for canonical correlation analysis.
KeywordsCanonical Correlation Analysis Normal Curvature Influence Function Multivariate Data Analysis Local Influence
Unable to display preview. Download preview PDF.
- BELSLEY, D. A., KUH, E. and WELSCH, R. E. (1980): Regression Diagnostics: Identifying Influential Data and Scources of Collinearity. John Wiley & Sons.Google Scholar
- COOK, R. D. (1986): Assessment of Local Influence. J. R. Statist Soc., B48, 133–169.Google Scholar
- COOK, R. D. and Weisberg, S. (1982): Residuals and Influence in Regression. Chapman and Hall.Google Scholar
- MAGNUS, J. R. and NEUDECKER, H. (1988): Matrix Differential Calculus with Applications in Statistics and Econometrics, John Wiley & Sons.Google Scholar
- SAS/STAT User’s Guide (1990): Version 6, Volume 1, SAS Institute Inc. Cary, NC, USAGoogle Scholar
- SEARLE, S. R. (1982): Matrix Algebra Useful for Statistics. John Wiley & Sons.Google Scholar
- SIOTANI, M., Hayakawa, T. and FUJIKOSHI, Y (1985): Modern Multivariate Statistical Analysis: A Graduate Course and Handbook. American Science Press, Inc.Google Scholar
- TANAKA, Y., Zhang, F. H. and Mori, Y. (1998): Influence in Principal Component Analysis Revisited, In Proceedings of the Third Conference on Statistical Computing of the Asian Regional Section of IASC, 319–330.Google Scholar
- ZHANG, F. H. and TANAKA, Y. (2001): A Note on the Assessment of Local Influence in Statistical Models with Equality Constraints. Technical Report, No. 74, Okayama Statistical Association, Okayama, Japan Google Scholar