The simplified component technique: An alternative to rotated principal components

Journal of Computational and Graphical Statistics

Volumn 9, Issue 4, 2000, Pages 689-710

  Jolliffe, Ian T ^a   Uddin, Mudassir ^a,b  

^a UNIVERSITY OF ABERDEEN   (United Kingdom)

^b UNIVERSITY OF KARACHI   (Pakistan)

Author keywords

Interpretation; Rotation; Simple structure

Indexed keywords

EID: 23044521947     PISSN: 10618600     EISSN: 15372715     Source Type: Journal    
DOI: 10.1080/10618600.2000.10474908     Document Type: Article

References (23)

1. Cadima, J., and Jolliffe, I. T. (1995), “Loadings and Correlations in the Interpretation of Principal Components,” Journal of Applied Statistics, 22, 203-214.
2. Gay, D. M. (1983), “Algorithm 611. Subroutines for Unconstrained Optimization Using a Model/Trust-Region Approach,” ACM Transactions on Mathematical Software, 9, 503-524.
3. Gay, D. M. (1984), “A Trust Region Approach to Linearly Constrained Optimization,” in Numerical Analysis. Proceedings, ed. F. A. Lootsma, New York: Springer, pp. 171-189.
4. Goffe, W. L., Ferrier, G. D., and Rogers, J. (1994), “Global Optimizations of Statistical Functions with Simu lated Annealing,” Journal of Econometrics, 60, 65-99.
5. Green, P. J., and Silverman, B. W. (1994), Nonparametric Regression and Generalised Linear Models: A Roughness Penalty Approach, London: Chapman and Hall.
6. Hausman, R. (1982), “Constrained Multivariate Analysis,” in Optimisation in Statistics, eds. S. H. Zanckis and J. S. Rustagi, Amsterdam: North Holland, pp. 137-151.
7. Huber, P. J. (1985), “Projection Pursuit” (with discussion), The Annals of Statistics, 13, 435-525.
8. Jolliffe, I. T. (1987), “Rotation of Principal Components: Some Comments,” Journal of Climatology, 1, 507 510.
9. Jolliffe, I. T. (1989), “Rotation of Ill-Defined Principal Components,” Applied Statistics, 38, 139-147.
10. Jolliffe, I. T. (1995), “Rotation of Principal Components: Choice of Normalization Constraints,” Journal of Applied Statistics, 22, 29-35.
11. Jolliffe, I. T., and Uddin, M. (in press), “A Modified Principal Component Technique Based on the Lasso,” submitted to Journal of Computational and Graphical Statistics.
12. Jones, M. C., and Sibson, R. (1987), “What is Projection Pursuit?” (with discussion), Journal of the Royal Statistical Society, Series A, 150, 1-36.
13. Krzanowski, W. J., and Marriott, F. H. C. (1995), Multivariate Analysis, Part II, London: Arnold.
14. Lundy, M., and Mees, A. (1986), “Convergence of an Annealing Algorithm,” Mathematical Programming, 34, 111-124.
15. Mitra, D., Romeo, F., and Sangiovanni-Vincentelli, A. L. (1986), “Convergence and Finite-Time Behaviour of Simulated Annealing,” Advances in Applied Probability, 18, 747-771.
16. Morton, S. C. (1989), “Interpretable Projection Pursuit,” Technical Report 106, Department of Statistics, Stan ford University, Stanford, California.
17. Rencher, A. C. (1995), Methods of Multivariate Analysis, New York: Wiley.
18. Rice, J. A., and Silverman, B. W. (1991) “Estimating the Mean and Covariance Structure Nonparametrically When the Data are Curves,” Journal of the Royal Statistical Society, Series B, 53, 233-243.
19. Richman, M. B. (1986), “Rotation of Principal Components,” Journal of Climatology, 6, 293-335.
20. Richman, M. B. (1987), “Rotation of Principal Components: A Reply,” Journal of Climatology, 1, 511-520.
21. Titterington, D. M. (1985) “Common Structure of Smoothing Techniques in Statistics,” International Statistical Review, 53, 141-170.
22. Uddin, M. (1999), “Interpretation of Results from Simplified Principal Components,” unpublished Ph. D. thesis, University of Aberdeen, Aberdeen, Scotland.
23. Vines, S. K. (2000), “Simple Principal Components,” Applied Statistics, 49, 441-451