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Editor: Universidad Carlos III de Madrid. Departamento de Estadística

Issued date: 2007-03

Serie-No.: UC3M Working papers. Statistics and Econometrics07-04

Keywords: Kurtosis , Projections , Robust covariance matrix , Stahel-Donoho estimator

Rights: Atribución-NoComercial-SinDerivadas 3.0 España

Abstract:Partial least squares regression (PLS) is a linear regression technique developed to relate manyregressors to one or several response variables. Robust methods are introduced to reduce orremove the effect of outlying data points. In this paper we show that iPartial least squares regression (PLS) is a linear regression technique developed to relate manyregressors to one or several response variables. Robust methods are introduced to reduce orremove the effect of outlying data points. In this paper we show that if the sample covariancematrix is properly robustified further robustification of the linear regression steps of the PLSalgorithm becomes unnecessary. The robust estimate of the covariance matrix is computed bysearching for outliers in univariate projections of the data on a combination of random directions(Stahel-Donoho) and specific directions obtained by maximizing and minimizing the kurtosiscoefficient of the projected data, as proposed by Peña and Prieto (2006). It is shown that thisprocedure is fast to apply and provides better results than other procedures proposed in theliterature. Its performance is illustrated by Monte Carlo and by an example, where the algorithm isable to show features of the data which were undetected by previous methods.+-





Author: González, Javier; Peña, Daniel; Romera, Rosario

Source: http://e-archivo.uc3m.es


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Universidad Carlos III de Madrid Repositorio institucional e-Archivo http:--e-archivo.uc3m.es Departamento de Estadística DES - Working Papers.
Statistics and Econometrics.
WS 2007-03 A robust partial least squares method with applications González, Javier http:--hdl.handle.net-10016-665 Descargado de e-Archivo, repositorio institucional de la Universidad Carlos III de Madrid Working Paper 07-13 Statistic and Econometric Series 04 March 2007 Departamento de Estadística Universidad Carlos III de Madrid Calle Madrid, 126 28903 Getafe (Spain) Fax (34-91) 6249849 A ROBUST PARTIAL LEAST SQUARES METHOD WITH APPLICATIONS∗ Javier González1, Daniel Peña 2 and Rosario Romera3 Abstract Partial least squares regression (PLS) is a linear regression technique developed to relate many regressors to one or several response variables.
Robust methods are introduced to reduce or remove the effect of outlying data points.
In this paper we show that if the sample covariance matrix is properly robustified further robustification of the linear regression steps of the PLS algorithm becomes unnecessary.
The robust estimate of the covariance matrix is computed by searching for outliers in univariate projections of the data on a combination of random directions (Stahel-Donoho) and specific directions obtained by maximizing and minimizing the kurtosis coefficient of the projected data, as proposed by Peña and Prieto (2006).
It is shown that this procedure is fast to apply and provides better results than other procedures proposed in the literature.
Its performance is illustrated by Monte Carlo and by an example, where the algorithm is able to show features of the data which were undetected by previous methods. Keywords: Kurtosis, projections, robust covariance matrix, Stahel-Donoho estimator. ∗ 1, 2, 3 Departamento de Estadística, Universidad Carlos III de Madrid, C- Madrid 126, 28903 Getafe, Madrid, Spain. This research has been supported by Spanish MEC grant SEJ2004...





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