Por favor, use este identificador para citar o enlazar este ítem:http://uvadoc.uva.es/handle/10324/18091
Título
Robust Principal Component Analysis Based On Trimming Around Affine Subspaces
Autor
Año del Documento
2016
Abstract
Principal Component Analysis (PCA) is a widely used technique for reducing
dimensionality of multivariate data. The principal component subspace is
defined as the affine subspace of a given dimension d giving the best fit to
the data. However, PCA suffers from a well-known lack of robustness. As a
robust alternative, one can resort to an impartial trimming based approach.
Here one searches for the best subsample containing a proportion 1 − α of
the observations, with 0 < α < 1, and the best d-dimensional affine subspace
fitting this subsample, yielding the trimmed principal component subspace.
A population version will be given and existence of a solution to both
the sample and population problem will be proven. Moreover, under mild
conditions, the solutions of the sample problem are consistent toward the
solutions of the population problem. The robustness of the method is studied by proving quantitative robustness, computing the breakdown point, and
deriving the influence functions. Furthermore, asymptotic efficiencies at the
normal model are derived, and finite sample efficiencies of the estimators are
studied by means of a simulation study
Materias (normalizadas)
Estadística
Departamento
Estadística e IO
Idioma
spa
Derechos
openAccess
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