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Abstract:

In this study, we introduce two families of robust kernel-based regression estimators when the regressors are random objects taking values in a Riemannian manifold. The first proposal is a local M-estimator based on kernel methods, adapted to the geometry of the manifold. For the second proposal, the weights are based on k-nearest neighbour kernel methods. Strong uniform consistent results as well as the asymptotical normality of both families are established. Finally, a Monte Carlo study is carried out to compare the performance of the robust proposed estimators with that of the classical ones, in normal and contaminated samples and a cross-validation method is discussed. © 2009 Taylor & Francis.

Registro:

Documento: Artículo
Título:Robust nonparametric regression on Riemannian manifolds
Autor:Henry, G.; Rodriguez, D.
Filiación:Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, Buenos Aires, C1428EHA, Argentina
Instituto de Cálculo, FCEyN, Universidad de Buenos Aires Ciudad Universitaria, Pabellón II, Buenos Aires, C1428EHA, Argentina
Palabras clave:K-nearest neighbour weights; Kernel weights; Nonparametric regression; Riemannian manifolds; Robust estimation
Año:2009
Volumen:21
Número:5
Página de inicio:611
Página de fin:628
DOI: http://dx.doi.org/10.1080/10485250902846439
Título revista:Journal of Nonparametric Statistics
Título revista abreviado:J. Nonparametric Stat.
ISSN:10485252
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10485252_v21_n5_p611_Henry

Referencias:

  • Nadaraya, E.A., On estimating regression (1964) Theory Probab. Appl., 9, pp. 141-142
  • Watson, G.S., Smooth regression analysis (1964) Sankhya Ser. A, 26, pp. 359-392
  • Collomb, G., Estimation de la regression par la méthode des k points les plus proches avec noyau: Quelques propiétés de convergence ponctuelle (1980) Lecture Notes in Mathematics, 821, pp. 159-175
  • Cleveland, W., Robust locally weighted regression and smoothing scatter plots (1979) J. Amer. Statist. Assoc., 74, pp. 829-836
  • Tsybakov, A.B., Robust estimates of a function (1982) Peredaci Informacii, 18, pp. 39-52
  • Tsybakov, A.B., Problems Inform Transmission, 18, pp. 190-201
  • Härdle, W., Robust regression function estimation (1984) J. Multivariate Anal., 14, pp. 169-180
  • Boente, G., Fraiman, R., Robust nonparametric regression estimation (1989) J. Multivariate Anal., 29, pp. 180-198
  • Härdle, W., (1990) Applied Nonparametric Regression, , Cambridge University Press
  • Mardia, K., Jupp, P., (2000) Directional Data, , Wiley, NewYork
  • Hall, P., Watson, G.S., Cabrera, J., Kernel density estimation with spherical data (1987) Biometrika, 74, pp. 751-762
  • Fischer, N.I., Lewis, T., Embleton, B.J.J., (1993) Statistical Analysis of Spherical Data, , Cambridge University Press
  • Lee, J.M., Ruymgaart, F.H., Nonparametric curve estimation on Stiefel manifolds (1996) J. Nonparametric Statist., 6, pp. 57-68
  • Hendriks, H., Nonparametric estimation of a probability density on a Riemannian manifold using Fourier expansions (1990) Ann. Statist., 18, pp. 832-849
  • Hendriks, H., Janssen, J.H.M., Ruymgaart, F.H., Strong uniform convergence of density estimators on compact Euclidean manifolds (1993) Statist. Probab. Lett., 16, pp. 305-311
  • Pelletier, B., Kernel density estimation on Riemannian maniflods (2005) Statist. Probab. Lett., 73, pp. 297-304
  • Pelletier, B., Nonparametric regression estimation on closed Riemannian manifolds (2006) J. Nonparametric Statist., 18, pp. 57-67
  • He, X., Robust statistics of directional data: A survey (1992) Nonparametric Statistics and Related Topics, pp. 87-95. , eds A. M. Saleh, North-Holland, NewYork
  • Ko, D., Guttorp, P., Robustness of estimators for directional data (1988) Ann. Statist., 16, pp. 609-618
  • Agostinelli, C., Robust estimation for circular data (2007) Comput. Statist. Data Anal., 51, pp. 5867-5875
  • Do Carmo, M., Geometria Riemaniana (1988) Proyecto Euclides, IMPA., , 2da edición
  • Berger, M., Gauduchon, P., Mazet, E., (1971) Le spectre d'une variété Riemannienne, , Springer-Verlag
  • Besse, A., (1978) Manifolds All of Whose Geodesics are Closed, , Springer-Verlag
  • Boothby, W.M., (2007) An Introduction to Differentiable Manifolds and Riemannian Geometry, , Academic Press, NewYork
  • He, X., Zhu, Z., Fung, W., Estimation in a semi parametric model for longitudinal data with unspecified dependence structure (2002) Biometrika, 89, pp. 579-590
  • Maronna, R., Martin, D., Yohai, V., (2006) Robust Statistics: Theory and Methods, , Wiley, NewYork
  • Wang, F., Scott, D., The L1 method for robust nonparametric regression (1994) J. Amer. Statist. Assoc., 89, pp. 65-76
  • Boente, G., Fraiman, R., Meloche, J., Robust plug-in bandwidth estimators in nonparametric regression (1997) J. Statist. Plann. Inference, 57, pp. 109-142
  • Cantoni, E., Ronchetti, E., Resistant selection of the smoothing parameter for smoothing splines (2001) Statist. Comput., 11, pp. 141-146
  • Leung, D., Cross-validation in nonparametric regression with outliers (2005) Ann. Statist., 33, pp. 2291-2310
  • Boente, G., Fraiman, R., Strong uniform convergence rates for some robust equivariant nonparametric regression estimates for mixing processes (1991) Int. Statist. Rev., 59, pp. 355-372
  • Boente, G., Fraiman, R., Asymptotic distribution of robust estimators for nonparametric models from mixing processes (1990) Ann. Statist., 18, pp. 891-906
  • Gray, A., Vanhecke, L., Riemannian geometry as determined by the volumes of small geodesic balls (1979) Acta Math., 142, pp. 157-198
  • Devroye, L., Wagner, T.J., The strong uniform consistency of nearest neighbour density estimates (1977) Ann. Statist., 3, pp. 536-540
  • Härdle, W., Tsybakov, A.B., Robust nonparametric regression with simultaneous scale curve estimation (1988) Ann. Statist., 16, pp. 120-135

Citas:

---------- APA ----------
Henry, G. & Rodriguez, D. (2009) . Robust nonparametric regression on Riemannian manifolds. Journal of Nonparametric Statistics, 21(5), 611-628.
http://dx.doi.org/10.1080/10485250902846439
---------- CHICAGO ----------
Henry, G., Rodriguez, D. "Robust nonparametric regression on Riemannian manifolds" . Journal of Nonparametric Statistics 21, no. 5 (2009) : 611-628.
http://dx.doi.org/10.1080/10485250902846439
---------- MLA ----------
Henry, G., Rodriguez, D. "Robust nonparametric regression on Riemannian manifolds" . Journal of Nonparametric Statistics, vol. 21, no. 5, 2009, pp. 611-628.
http://dx.doi.org/10.1080/10485250902846439
---------- VANCOUVER ----------
Henry, G., Rodriguez, D. Robust nonparametric regression on Riemannian manifolds. J. Nonparametric Stat. 2009;21(5):611-628.
http://dx.doi.org/10.1080/10485250902846439