José Carlos Vega–Vilca^*
Josué Guzmán^†

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Resumen ]]>
Se presentan y comparan las técnicas de regresión por componentes principales y la regresión por componentes desde mínimos cuadrados parciales, como solución al problema de multicolinealidad en regresión múltiple. Se ilustran las metodologías con  ejemplos de aplicación en la que se observa la superioridad de la técnica por
mínimos cuadrados parciales.

Palabras clave: análisis de componentes principales, mínimos cuadrados parciales, reducción de la dimensionalidad.

Abstract

We present and compare principal components regression and partial least squares  regression, and their solution to the problem of multicollinearity. We illustrate the use  of both techniques, and demonstrate the superiority of partial least squares.

Keywords: principal components analysis, partial least squares, dimensionality reduction.

Mathematics Subject Classification: 62H25, 62J02.

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Referencias

[1] Frank, I.E.; Friedman, J.H. (1993) “A statistical view of some chemometrics regression tools”, Technometrics 35:109–148.         [ Links ]

[2] Garthwaite, P.H. (1994) “An interpretation of partial least square regression”, Journal of the American Statistical Association 89(425): 122–127.         [ Links ]

[3] Helland, I. (1988) “On the structure of partial least squares regression”, Communications in Statistics, Simulation and Computation, 17(2): 581–607.         [ Links ]

[4] Hoskulsson, A. (1988) “PLS regression methods”, Chemometrics, 2: 211–228.         [ Links ]

[5] Mardia, K.V.; Kent, J.T.; Bibby, J.M. (1997) Multivariate Analysis. Academic Press, London.         [ Links ]

[6] Massy, W.F. (1965) “Principal Components Regression in Exploratory Statistical Research”, Journal of the American Statistical Association, 60: 234–246.         [ Links ]

[7] Stone, M.; Brooks, R.J. (1990) “Continuum regression: crossvalidated sequentially constructed prediction embracing ordinary least squares, partial least squares and  principal components regression”, Journal of the Royal Statistical Society 52: 237–269.         [ Links ]

[8] Trygg, J. (2001) Parsimonious Multivariate Models. PhD Thesis, Umea University, Research Group for Chemometrics Department of Chemistry.         [ Links ] ]]>

[9] Wold, H. (1975) “Soft modeling by latent variables; the nonlinear iterative partial least square approach”, Perspectives in Probability and Statistics, Papers in Honour of M.S. Bartlett.         [ Links ]

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Received: 18 Feb 2010; Revised: 5 Aug 2010; Accepted: 14 Aug 2010