The peculiar shrinkage properties of partial least squares regression

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 62, Issue 3, 2000, Pages 585-593

  Butler, Neil A ^a   Denham, Michael C ^b  

^a UNIVERSITY OF READING   (United Kingdom)

^b NONE

Author keywords

Ordinary least squares; Partial least squares; Principal components; Regularized regression; Ridge regression

Indexed keywords

EID: 0034355177     PISSN: 13697412     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9868.00252     Document Type: Article

References (11)

1. Brown, P. J. (1990) Partial least squares in perspective. Anal. Proc. R. Soc. Chem., 27, 303-306.
2. _ (1993) Measurement, Regression, and Calibration. Oxford: Clarendon.
3. Denham, M. C. (1991) Calibration in infrared spectroscopy. PhD Thesis. University of Liverpool, Liverpool.
4. Frank, I. E. and Friedman, J. H. (1993) A statistical view of some chemometrics tools. Technometrics, 35, 109-135.
5. Goutis, C. (1996) Partial least squares yields shrinkage estimators. Ann. Statist., 24, 816-824.
6. Helland, I. (1988) On the structure of partial least squares regression. Communs Statist. Simuln Computn, 17, 581-607.
7. Martens, H. and Jensen, S. A. (1983) Partial least squares regression: a new two-stage NIR calibration method. In Progress in Cereal Chemistry and Technology: Proc. 7th Wrld Cereal and Bread Congr. Prague, June 1982 (eds J. Holas and J. Kratochvil), pp. 607-647. Amsterdam: Elsevier.
8. Stone, M. and Brooks, R. J. (1990) Continuum regression: cross-validated sequentially constructed prediction embracing ordinary least squares, partial least squares and principal components regression (with discussion). J. R. Statist. Soc. B, 52, 237-269.
9. Wold, H. (1966) Nonlinear estimation by iterative least squares procedures. In Research Papers in Statistics: Festschrift for J. Neyman (ed. F. N. David), pp. 411-444. New York: Wiley.
10. _ (1973) Nonlinear iterative partial least squares (NIPALS) modelling: some current developments. In Multivariate Analysis III (ed. P. Krishnaiah), pp. 383-407. New York: Academic Press.
11. _ (1982) Soft modeling: the basic design and some extensions. In Systems under Indirect Observation: Causality-Structure-Prediction (eds K. G. Jöreskog and H. Wold), vol. II, ch. 1, pp. 1-54. Amsterdam: North-Holland.