Abstract
Many multivariate techniques such as principal component analysis, dual scaling and discriminant analysis can be formulated as eigenvalue problems, including generalized eigenvalue problems. This paper introduces a sensitivity analysis method developing the idea of W.S. De Sarbo, et al., who proposed the use of an ε-neighborhood around the maximum value of the criterion function. They and W.J. Krzanowski derived an approximate e-neighborhood. This paper presents the exact ε-neighborhood. As application examples of the exact ε-neighborhood, dual scaling for conditional ordinal data and principal component analysis are discussed.
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References
De Sarbo, W.S., Hausman, R.E., Lin, S., Thompson, W. (1982). Constrained canonical correlation; Psychometrika, 47, 489–516.
Krzanowski, W.J. (1984). Sensitivity of principal components; Journal of the Royal Statistical Society, 46, 558–563.
Nishisato, S. (1980). Analysis of Categorical Data: Dual Scaling and Its Applications; Univ. of Toronto Press, Chap. 6.
Okuno, T., Kume, H., Haga, T., Yoshizawa, T. (1981). Tahenryou Kaisekihou (Multivariate Analysis), Revised Version, Union of Japanese Scientists and Engineers, 195–206. (in Japanese).
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Ueda, T. Sensitivity Analysis in Eigenvalue Problems and its Application to Conditional Ordinal Data. Behaviormetrika 15, 93–109 (1988). https://doi.org/10.2333/bhmk.15.23_93
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DOI: https://doi.org/10.2333/bhmk.15.23_93