## Electronic Journal of Statistics

### Sensitivity of principal component subspaces: A comment on Prendergast’s paper

Jacques Bénasséni

#### Abstract

In a recent paper on sensitivity of subspaces spanned by principal components, [5] introduces an influence measure based on second order expansion of the RV and GCD coefficients which are commonly used as measures of similarity between two matrices. The goal of this short note is to point out that the paper of [2] is based on a similar approach. However this work seems unknown to Prendergast since it is missing in his references. A comparison of the two papers is provided together with a brief review of some related works.

#### Article information

Source
Electron. J. Statist., Volume 8, Number 1 (2014), 927-930.

Dates
First available in Project Euclid: 29 July 2014

https://projecteuclid.org/euclid.ejs/1406638929

Digital Object Identifier
doi:10.1214/14-EJS915

Mathematical Reviews number (MathSciNet)
MR3263107

Zentralblatt MATH identifier
1349.62246

Subjects
Primary: 62F35: Robustness and adaptive procedures
Secondary: 62H12: Estimation

#### Citation

Bénasséni, Jacques. Sensitivity of principal component subspaces: A comment on Prendergast’s paper. Electron. J. Statist. 8 (2014), no. 1, 927--930. doi:10.1214/14-EJS915. https://projecteuclid.org/euclid.ejs/1406638929

#### References

• [1] Bénasséni, J. (1990). Sensitivity coefficients for the subspaces spanned by principal components. Commun. Statist.-Theory Methods 19 2021–2034.
• [2] Castaño-Tostado, E. and Tanaka, Y. (1990). Some comments on Escoufier’s $RV$-coefficient as a sensitivity measure in principal component analysis. Commun. Statist.-Theory Methods 19 4619–4626.
• [3] Critchley, F. (1985). Influence in principal component analysis. Biometrika 72 627–636.
• [4] Hampel, F. R. (1974). The influence curve and its role in robust estimation. J. Amer. Statist. Assoc. 69 383–393.
• [5] Prendergast, L. A. (2008). A note on sensitivity of principal component subspaces and the efficient detection of influential observations in high dimensions. Electron. J. Statist. 2 454–467.
• [6] Prendergast, L. A. and Li Wai Suen, C. (2011). A new and practical influence measure for subsets of covariance matrix sample principal components with applications to high dimensional datasets. Comput. Statist. Data Anal. 55 752–764.
• [7] Tanaka, Y. (1988). Sensitivity analysis in principal component analysis: influence on the subspace spanned by principal components. Commun. Statist.-Theory Methods 17 3157–3175.
• [8] Tanaka, Y. and Castaño-Tostado, E. (1990). Quadratic perturbation expansions of certain functions of eigenvalues and eigenvectors and their application to sensitivity analysis in multivariate methods. Commun. Statist.-Theory Methods 19 2943–2965.