Goutis, Constantinos Partial least squares algorithm yields shrinkage estimators. (English) Zbl 0859.62067 Ann. Stat. 24, No. 2, 816-824 (1996). Summary: 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. Cited in 15 Documents MSC: 62J07 Ridge regression; shrinkage estimators (Lasso) 62H12 Estimation in multivariate analysis Keywords:biased estimation; chemometrics; collinearity; data compression methods; geometric proof; ordinary least squares estimates; sequential construction algorithm of partial least squares; shrinkage × Cite Format Result Cite Review PDF Full Text: DOI References: [1] DE JONG, S. 1995. PLS shrinks. Journal of Chemometrics 9 323 326. Z. [2] DENHAM, M. C. 1991. Calibration in infrared spectroscopy. Ph.D. dissertation, Univ. Liverpool. Z. [3] FRANK, I. E. and FRIEDMAN, J. H. 1993. A statistical view of some chemometrics regression tools Z. with discussion. Technometrics 35 109 147. Z. · Zbl 0775.62288 · doi:10.2307/1269656 [4] HELLAND, I. S. 1988. On the structure of partial least squares regression. Comm. Statist. Simulation Comput. 17 581 607. Z. · Zbl 0695.62167 · doi:10.1080/03610918808812681 [5] MARTENS, H. and NAES, T. 1989. Multivariate Calibration. Wiley, New York. Z. [6] NAES, T. and MARTENS, H. 1985. Comparison of prediction methods for multicollinear data. Comm. Statist. Simulation Comput. 14 545 576. · Zbl 0576.62072 · doi:10.1080/03610918508812458 [7] 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. · Zbl 0775.62175 · doi:10.1080/03610929208830862 [8] SCHEFFE, H. 1959. The Analy sis of Variance. Wiley, New York. Ź. [9] 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. JSTOR: · Zbl 0708.62054 [10] SUNDBERG, R. 1993. Continuum regression and ridge regression. J. Roy. Statist. Soc. Ser. B 55 653 659. Z. JSTOR: · Zbl 0783.62049 [11] 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. · Zbl 0161.15901 [12] 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. · Zbl 0296.62097 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.