RT info:eu-repo/semantics/preprint
T1 Robust Principal Component Analysis Based On Trimming Around Affine Subspaces
A1 Croux, Christophe
A1 García Escudero, Luis Ángel
A1 Gordaliza Ramos, Alfonso
A1 Ruwet, Christel
A1 San Martín Fernández, Roberto
K1 Estadística
AB Principal Component Analysis (PCA) is a widely used technique for reducingdimensionality of multivariate data. The principal component subspace isdefined as the affine subspace of a given dimension d giving the best fit tothe data. However, PCA suffers from a well-known lack of robustness. As arobust alternative, one can resort to an impartial trimming based approach.Here one searches for the best subsample containing a proportion 1 − α ofthe observations, with 0 < α < 1, and the best d-dimensional affine subspacefitting this subsample, yielding the trimmed principal component subspace.A population version will be given and existence of a solution to boththe sample and population problem will be proven. Moreover, under mildconditions, the solutions of the sample problem are consistent toward thesolutions of the population problem. The robustness of the method is studied by proving quantitative robustness, computing the breakdown point, andderiving the influence functions. Furthermore, asymptotic efficiencies at thenormal model are derived, and finite sample efficiencies of the estimators arestudied by means of a simulation study
YR 2016
FD 2016
LK http://uvadoc.uva.es/handle/10324/18091
UL http://uvadoc.uva.es/handle/10324/18091
LA spa
NO Estadística e IO
DS UVaDOC
RD 07-ago-2024