Abstract
The perturbation theory provides a useful tool for the sensitivity analysis in linear discriminant analysis (LDA). Though some influence functions by single perturbation and local influence in LDA have been discussed in literature, we propose yet another influence function inspired by Critchley [1985. Influence in principal component analysis. Biometrika 72, 627-636], called the deleted empirical influence function, as an alternative approach for the influence analysis in LDA. It is well-known that single-perturbation diagnostics can suffer from the masking effect. Hence in this paper we also develop the pair-perturbation influence functions to detect the masked influential points. The comparisons between pair-perturbation influence functions and local influences in pairs in LDA are also investigated. Finally, two examples are provided to illustrate the results of these approaches.
| Original language | English |
|---|---|
| Pages (from-to) | 3844-3861 |
| Number of pages | 18 |
| Journal | Computational Statistics and Data Analysis |
| Volume | 51 |
| Issue number | 8 |
| DOIs | |
| Publication status | Published - 2007 May 1 |
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All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Computational Mathematics
- Computational Theory and Mathematics
- Applied Mathematics
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Influence functions and local influence in linear discriminant analysis. / Huang, Yufen; Kao, Tzu Ling; Wang, Tai Ho.
In: Computational Statistics and Data Analysis, Vol. 51, No. 8, 01.05.2007, p. 3844-3861.Research output: Contribution to journal › Article
TY - JOUR
T1 - Influence functions and local influence in linear discriminant analysis
AU - Huang, Yufen
AU - Kao, Tzu Ling
AU - Wang, Tai Ho
PY - 2007/5/1
Y1 - 2007/5/1
N2 - The perturbation theory provides a useful tool for the sensitivity analysis in linear discriminant analysis (LDA). Though some influence functions by single perturbation and local influence in LDA have been discussed in literature, we propose yet another influence function inspired by Critchley [1985. Influence in principal component analysis. Biometrika 72, 627-636], called the deleted empirical influence function, as an alternative approach for the influence analysis in LDA. It is well-known that single-perturbation diagnostics can suffer from the masking effect. Hence in this paper we also develop the pair-perturbation influence functions to detect the masked influential points. The comparisons between pair-perturbation influence functions and local influences in pairs in LDA are also investigated. Finally, two examples are provided to illustrate the results of these approaches.
AB - The perturbation theory provides a useful tool for the sensitivity analysis in linear discriminant analysis (LDA). Though some influence functions by single perturbation and local influence in LDA have been discussed in literature, we propose yet another influence function inspired by Critchley [1985. Influence in principal component analysis. Biometrika 72, 627-636], called the deleted empirical influence function, as an alternative approach for the influence analysis in LDA. It is well-known that single-perturbation diagnostics can suffer from the masking effect. Hence in this paper we also develop the pair-perturbation influence functions to detect the masked influential points. The comparisons between pair-perturbation influence functions and local influences in pairs in LDA are also investigated. Finally, two examples are provided to illustrate the results of these approaches.
UR - http://www.scopus.com/inward/record.url?scp=34047125237&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=34047125237&partnerID=8YFLogxK
U2 - 10.1016/j.csda.2006.03.001
DO - 10.1016/j.csda.2006.03.001
M3 - Article
VL - 51
SP - 3844
EP - 3861
JO - Computational Statistics and Data Analysis
JF - Computational Statistics and Data Analysis
SN - 0167-9473
IS - 8
ER -