Abstract
A second order approximation to the sample influence curve (SIC) in canonical correlation analysis has been derived in the literature. However, it does not seem satisfactory for some cases. In this paper, we present a more accurate second order approximation. As a particular case, the proposed method is exact for the SIC of the squared multiple correlation coefficient. An example is given.
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Calder, P. (1986).Influence functions in multivariate analysis. Unpublished doctoral dissertation, University of Kent.
Cook, R. D., & Weisberg, S. (1982).Residuals and influence in regression. New York: Chapman and Hall.
Hoaglin, D. C., & Welsch, R. E. (1978). The hat matrix in regression and ANOVA.The American Statistician, 32, 17–22.
Radhakrishnan, R., & Kshirsagar, A. M. (1981). Influence functions for certain parameters in multivariate analysis.Communications in Statistics—Theory and Methods, 10, 515–529.
Romanazzi, M. (1991). Influence in canonical variates analysis.Computational Statistics & Data Analysis, 11, 143–164.
Romanazzi, M. (1992). Influence in canonical correlation analysis.Psychometrika, 57, 237–259.
SAS Institute. SAS/STAT User's Guide (1990), Version 6, Volume 1. Cary, NC: Author.
Tanaka, Y. (1994). Recent advance in sensitivity analysis in multivariate statistical methods.Journal of Japanese Society of Computational Statistics, 7, 1–25.
Tanaka, Y., & Odaka, Y. (1989). Influenctial observations in principal factor analysis.Psychometrika, 54, 475–485.
Wilkinson, J. H. (1965).The algebraic eigenvalue problem. Oxford: Clarendon Press.
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The authors are most grateful to the associate editor and three reviewers for valuable comments and suggestions which improved the presentation of the paper considerably. The first author was partly supported by a RGC earmarked research grant of Hong Kong.
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Fung, W.K., Gu, H. The second order approximation to sample influence curve in canonical correlation analysis. Psychometrika 63, 263–269 (1998). https://doi.org/10.1007/BF02294855
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DOI: https://doi.org/10.1007/BF02294855