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Abstract:

All known approaches to nonlinear principal components are based on minimizing a quadratic loss, which makes them sensitive to data contamination. A predictive approach in which a spline curve is fit minimizing a residual M-scale is proposed for this problem. For a p-dimensional random sample xi (i=1,…,n) the method finds a function h:R→Rp and a set {t1,…,tn}⊂R that minimize a joint M-scale of the residuals xi−h(ti), where h ranges on the family of splines with a given number of knots. The computation of the curve then becomes the iterative computing of regression S-estimators. The starting values are obtained from a robust linear principal components estimator. A simulation study and the analysis of a real data set indicate that the proposed approach is almost as good as other proposals for row-wise contamination, and is better for element-wise contamination. © 2013, Springer Science+Business Media New York.

Registro:

Documento: Artículo
Título:Robust nonlinear principal components
Autor:Maronna, R.A.; Méndez, F.; Yohai, V.J.
Filiación:University of La Plata, C.C. 172, La Plata, 1900, Argentina
University of Rosario, Bv. Oroño 1261, Rosario, 2000, Argentina
Departamento de Matemática, Universidad de Buenos Aires, Ciudad Universitaria, Pabellon 1, Buenos Aires, 1428, Argentina
Palabras clave:Principal curves; S-estimators; Splines
Año:2013
Volumen:25
Número:2
Página de inicio:439
Página de fin:448
DOI: http://dx.doi.org/10.1007/s11222-013-9442-0
Título revista:Statistics and Computing
Título revista abreviado:Stat. Comput.
ISSN:09603174
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09603174_v25_n2_p439_Maronna

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Citas:

---------- APA ----------
Maronna, R.A., Méndez, F. & Yohai, V.J. (2013) . Robust nonlinear principal components. Statistics and Computing, 25(2), 439-448.
http://dx.doi.org/10.1007/s11222-013-9442-0
---------- CHICAGO ----------
Maronna, R.A., Méndez, F., Yohai, V.J. "Robust nonlinear principal components" . Statistics and Computing 25, no. 2 (2013) : 439-448.
http://dx.doi.org/10.1007/s11222-013-9442-0
---------- MLA ----------
Maronna, R.A., Méndez, F., Yohai, V.J. "Robust nonlinear principal components" . Statistics and Computing, vol. 25, no. 2, 2013, pp. 439-448.
http://dx.doi.org/10.1007/s11222-013-9442-0
---------- VANCOUVER ----------
Maronna, R.A., Méndez, F., Yohai, V.J. Robust nonlinear principal components. Stat. Comput. 2013;25(2):439-448.
http://dx.doi.org/10.1007/s11222-013-9442-0