Premium
On estimation of multivariate prediction regions in partial least squares regression
Author(s) -
Lin Weilu,
Zhuang Yingping,
Zhang Siliang,
Martin Elaine
Publication year - 2013
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/cem.2530
Subject(s) - partial least squares regression , multivariate statistics , linearization , mathematics , jacobian matrix and determinant , statistics , matrix (chemical analysis) , computer science , algorithm , chemistry , chromatography , nonlinear system , physics , quantum mechanics
The estimation of the prediction region of partial least squares (PLS) is necessary in many engineering applications. However, research in this area focuses on the estimation of prediction intervals only. In this work, a new recursive formulation of PLS is proposed to facilitate the calculation of the Jacobian matrix of the estimated coefficient matrix. Furthermore, the computational complexity analysis indicates that the proposed algorithm is O ( m 2 N + mpN + mpN 2 + mN 3 + mpN 4 ) per number of component. The prediction region of the multivariate PLS is obtained through local linearization. The new formulation provides one way to obtain the prediction region of the multivariate PLS. Simulation and near‐infrared spectra of corn case studies indicate the utility of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.