Robust nonparametric regression on Riemannian manifolds

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, th...

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Detalles Bibliográficos
Autores principales:	Henry, Guillermo Sebastián, Rodríguez, Daniela Andrea
Publicado:	2009
Materias:	K-nearest neighbour weights Kernel weights Nonparametric regression Riemannian manifolds Robust estimation
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10485252_v21_n5_p611_Henry http://hdl.handle.net/20.500.12110/paper_10485252_v21_n5_p611_Henry
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_10485252_v21_n5_p611_Henry
record_format	dspace
spelling	paper:paper_10485252_v21_n5_p611_Henry2023-06-08T16:01:19Z Robust nonparametric regression on Riemannian manifolds Henry, Guillermo Sebastián Rodríguez, Daniela Andrea K-nearest neighbour weights Kernel weights Nonparametric regression Riemannian manifolds Robust estimation 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. Fil:Henry, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Rodriguez, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2009 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10485252_v21_n5_p611_Henry http://hdl.handle.net/20.500.12110/paper_10485252_v21_n5_p611_Henry
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	K-nearest neighbour weights Kernel weights Nonparametric regression Riemannian manifolds Robust estimation
spellingShingle	K-nearest neighbour weights Kernel weights Nonparametric regression Riemannian manifolds Robust estimation Henry, Guillermo Sebastián Rodríguez, Daniela Andrea Robust nonparametric regression on Riemannian manifolds
topic_facet	K-nearest neighbour weights Kernel weights Nonparametric regression Riemannian manifolds Robust estimation
description	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.
author	Henry, Guillermo Sebastián Rodríguez, Daniela Andrea
author_facet	Henry, Guillermo Sebastián Rodríguez, Daniela Andrea
author_sort	Henry, Guillermo Sebastián
title	Robust nonparametric regression on Riemannian manifolds
title_short	Robust nonparametric regression on Riemannian manifolds
title_full	Robust nonparametric regression on Riemannian manifolds
title_fullStr	Robust nonparametric regression on Riemannian manifolds
title_full_unstemmed	Robust nonparametric regression on Riemannian manifolds
title_sort	robust nonparametric regression on riemannian manifolds
publishDate	2009
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10485252_v21_n5_p611_Henry http://hdl.handle.net/20.500.12110/paper_10485252_v21_n5_p611_Henry
work_keys_str_mv	AT henryguillermosebastian robustnonparametricregressiononriemannianmanifolds AT rodriguezdanielaandrea robustnonparametricregressiononriemannianmanifolds
_version_	1768543144485322752

Robust nonparametric regression on Riemannian manifolds

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