Partial least squares algorithm yields shrinkage estimators
Constantinos Goutis
Source: Ann. Statist. Volume 24, Number 2
(1996), 816-824.
Abstract
We give a geometric proof that the estimates of a regression model derived by using partial least squares shrink the ordinary least squares estimates. The proof is based on a sequential construction algorithm of partial least squares. A discussion of the nature of shrinkage is included.
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Keywords: Biased estimation; chemometrics; collinearity; data compression methods; ordinary least squares; regression
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aos/1032894467
Mathematical Reviews number (MathSciNet): MR1394990
Digital Object Identifier: doi:10.1214/aos/1032894467
Zentralblatt MATH identifier: 0859.62067
References
DE JONG, S. 1995. PLS shrinks. Journal of Chemometrics 9 323 326. Z.
DENHAM, M. C. 1991. Calibration in infrared spectroscopy. Ph.D. dissertation, Univ. Liverpool. Z.
FRANK, I. E. and FRIEDMAN, J. H. 1993. A statistical view of some chemometrics regression tools Z. with discussion. Technometrics 35 109 147. Z.
HELLAND, I. S. 1988. On the structure of partial least squares regression. Comm. Statist. Simulation Comput. 17 581 607. Z.
Mathematical Reviews (MathSciNet): MR90a:62176
Zentralblatt MATH: 0695.62167
Digital Object Identifier: doi:10.1080/03610918808812681
MARTENS, H. and NAES, T. 1989. Multivariate Calibration. Wiley, New York. Z.
Mathematical Reviews (MathSciNet): MR91e:62050
NAES, T. and MARTENS, H. 1985. Comparison of prediction methods for multicollinear data. Comm. Statist. Simulation Comput. 14 545 576.
Zentralblatt MATH: 0576.62072
PHATAK, A., REILLY, P. M. and PENLIDIS, A. 1992. The geometry of 2-block partial least squares regression. Comm. Statist. Theory Methods 21 1517 1553. Z.
Mathematical Reviews (MathSciNet): MR1173313
Zentralblatt MATH: 0775.62175
Digital Object Identifier: doi:10.1080/03610929208830862
SCHEFFE, H. 1959. The Analy sis of Variance. Wiley, New York. ´ Z.
Mathematical Reviews (MathSciNet): MR22:7217
STONE, M. and BROOKS, R. J. 1990. Continuum regression: cross-validated sequentially constructed prediction embracing ordinary least squares, partial least squares and princiZ. pal components regression with discussion. J. Roy. Statist. Soc. Ser. B 52 237 269. Z.
Mathematical Reviews (MathSciNet): MR1064418
JSTOR: links.jstor.org
SUNDBERG, R. 1993. Continuum regression and ridge regression. J. Roy. Statist. Soc. Ser. B 55 653 659. Z.
Mathematical Reviews (MathSciNet): MR94a:62108
JSTOR: links.jstor.org
WOLD, H. 1966. Nonlinear estimation by iterative least squares procedures. In Research Papers Z. in Statistics. Festschrift for J. Ney man F. N. David, ed. 411 444. Wiley, New York. Z. Z.
Mathematical Reviews (MathSciNet): MR35:1144
Zentralblatt MATH: 0161.15901
WOLD, H. 1973. Nonlinear iterative partial least squares NIPALS modelling: some current Z. developments. In Multivariate Analy sis P. R. Krishnaiah, ed. 3 383 407. Academic Press, New York.
Mathematical Reviews (MathSciNet): MR49:8228
Zentralblatt MATH: 0296.62097
