Robust nonlinear principal components
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=...
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| Autores principales: | , , |
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| Formato: | JOUR |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_09603174_v25_n2_p439_Maronna |
| Aporte de: |
| Sumario: | 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. |
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