Robust estimators under a functional common principal components model

Authors
Bali, Juan Lucas; Boente Boente, Graciela Lina
Publication Year
2017
Language
English
Format
article
Status
Published version
Description
When dealing with several populations of functional data, equality of the covariance operators is often assumed even when seeking for a lower-dimensional approximation to the data. Usually, if this assumption does not hold, one estimates the covariance operator of each group separately, which leads to a large number of parameters. As in the multivariate setting, this is not satisfactory since the covariance operators may exhibit some common structure, as is, for instance, the assumption of common principal directions. The existing procedures to estimate the common directions are sensitive to atypical observations. For that reason, robust projection-pursuit estimators for the common directions under a common principal component model are considered. A numerical method to compute the first directions is also provided. Under mild conditions, consistency results are obtained. A Monte Carlo study is performed to compare the finite sample behaviour of the estimators based on robust scales and on the standard deviation. The usefulness of the proposed approach is illustrated on a real data set.
Fil: Bali, Juan Lucas. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Ministerio de Defensa. Instituto de Investigaciones Científicas y Técnicas para la Defensa; Argentina. Universidad de Buenos Aires; Argentina. Universidad Nacional de San Martín; Argentina
Fil: Boente Boente, Graciela Lina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires; Argentina
Subject
COMMON PRINCIPAL COMPONENT MODEL
FISHER-CONSISTENCY
FUNCTIONAL DATA ANALYSIS
OUTLIERS
PROJECTION-PURSUIT
ROBUST ESTIMATION
Matemática Pura
Matemáticas
CIENCIAS NATURALES Y EXACTAS
Access level
Restricted access
License
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repository
CONICET Digital (CONICET)
Institution
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identifier
oai:ri.conicet.gov.ar:11336/63020