Title 



Partial robust Mregression
 
Author 



 
Abstract 



Partial Least Squares (PLS) is a standard statistical method in chemometrics. It can be considered as an incomplete, or partial, version of the Least Squares estimator of regression, applicable when high or perfect multicollinearity is present in the predictor variables. The Least Squares estimator is wellknown to be an optimal estimator for regression, but only when the error terms are normally distributed. In the absence of normality, and in particular when outliers are in the data set, other more robust regression estimators have better properties. In this paper a partial version of Mregression estimators will be defined. If an appropriate weighting scheme is chosen, partial Mestimators become entirely robust to any type of outlying points, and are called Partial Robust Mestimators. It is shown that partial robust Mregression outperforms existing methods for robust PLS regression in terms of statistical precision and computational speed, while keeping good robustness properties. The method is applied to a data set consisting of EPXMA spectra of archaeological glass vessels. This data set contains several outliers, and the advantages of partial robust Mregression are illustrated. Applying partial robust Mregression yields much smaller prediction errors for noisy calibration samples than PLS. On the other hand, if the data follow perfectly well a normal model, the loss in efficiency to be paid for is very small.   
Language 



English
 
Source (journal) 



Chemometrics and intelligent laboratory systems.  Amsterdam  
Publication 



Amsterdam : 2005
 
ISSN 



01697439
 
Volume/pages 



79:1/2(2005), p. 5564
 
ISI 



000232000300006
 
Full text (Publisher's DOI) 


  
