S-Estimators for Functional Principal Component Analysis

Principal component analysis is a widely used technique that provides an optimal lower-dimensional approximation to multivariate or functional datasets. These approximations can be very useful in identifying potential outliers among high-dimensional or functional observations. In this article, we pr...

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Autores principales: Boente, G., Salibian-Barrera, M.
Formato: JOUR
Materias:
Functional data analysis
Robust estimation
Sparse data
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_01621459_v110_n511_p1100_Boente
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_01621459_v110_n511_p1100_Boente
record_format dspace
spelling todo:paper_01621459_v110_n511_p1100_Boente2023-10-03T15:01:31Z S-Estimators for Functional Principal Component Analysis Boente, G. Salibian-Barrera, M. Functional data analysis Robust estimation Sparse data Principal component analysis is a widely used technique that provides an optimal lower-dimensional approximation to multivariate or functional datasets. These approximations can be very useful in identifying potential outliers among high-dimensional or functional observations. In this article, we propose a new class of estimators for principal components based on robust scale estimators. For a fixed dimension q, we robustly estimate the q-dimensional linear space that provides the best prediction for the data, in the sense of minimizing the sum of robust scale estimators of the coordinates of the residuals. We also study an extension to the infinite-dimensional case. Our method is consistent for elliptical random vectors, and is Fisher consistent for elliptically distributed random elements on arbitrary Hilbert spaces. Numerical experiments show that our proposal is highly competitive when compared with other methods. We illustrate our approach on a real dataset, where the robust estimator discovers atypical observations that would have been missed otherwise. Supplementary materials for this article are available online. © 2015, © American Statistical Association. Fil:Boente, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_01621459_v110_n511_p1100_Boente
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Functional data analysis
Robust estimation
Sparse data
spellingShingle Functional data analysis
Robust estimation
Sparse data
Boente, G.
Salibian-Barrera, M.
S-Estimators for Functional Principal Component Analysis
topic_facet Functional data analysis
Robust estimation
Sparse data
description Principal component analysis is a widely used technique that provides an optimal lower-dimensional approximation to multivariate or functional datasets. These approximations can be very useful in identifying potential outliers among high-dimensional or functional observations. In this article, we propose a new class of estimators for principal components based on robust scale estimators. For a fixed dimension q, we robustly estimate the q-dimensional linear space that provides the best prediction for the data, in the sense of minimizing the sum of robust scale estimators of the coordinates of the residuals. We also study an extension to the infinite-dimensional case. Our method is consistent for elliptical random vectors, and is Fisher consistent for elliptically distributed random elements on arbitrary Hilbert spaces. Numerical experiments show that our proposal is highly competitive when compared with other methods. We illustrate our approach on a real dataset, where the robust estimator discovers atypical observations that would have been missed otherwise. Supplementary materials for this article are available online. © 2015, © American Statistical Association.
format JOUR
author Boente, G.
Salibian-Barrera, M.
author_facet Boente, G.
Salibian-Barrera, M.
author_sort Boente, G.
title S-Estimators for Functional Principal Component Analysis
title_short S-Estimators for Functional Principal Component Analysis
title_full S-Estimators for Functional Principal Component Analysis
title_fullStr S-Estimators for Functional Principal Component Analysis
title_full_unstemmed S-Estimators for Functional Principal Component Analysis
title_sort s-estimators for functional principal component analysis
url http://hdl.handle.net/20.500.12110/paper_01621459_v110_n511_p1100_Boente
work_keys_str_mv AT boenteg sestimatorsforfunctionalprincipalcomponentanalysis
AT salibianbarreram sestimatorsforfunctionalprincipalcomponentanalysis
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