Detecting influential observations in principal components and common principal components

Authors
Boente Boente, Graciela Lina; Pires, Ana M.; Rodrigues, Isabel M.
Publication Year
2010
Language
English
Format
article
Status
Published version
Description
Detecting outlying observations is an important step in any analysis, even when robust estimates are used. In particular, the robustified Mahalanobis distance is a natural measure of outlyingness if one focuses on ellipsoidal distributions. However, it is well known that the asymptotic chi-square approximation for the cutoff value of the Mahalanobis distance based on several robust estimates (like the minimum volume ellipsoid, the minimum covariance determinant and the S-estimators) is not adequate for detecting atypical observations in small samples from the normal distribution. In the multi-population setting and under a common principal components model, aggregated measures based on standardized empirical influence functions are used to detect observations with a significant impact on the estimators. As in the one-population setting, the cutoff values obtained from the asymptotic distribution of those aggregated measures are not adequate for small samples. More appropriate cutoff values, adapted to the sample sizes, can be computed by using a cross-validation approach. Cutoff values obtained from a Monte Carlo study using S-estimators are provided for illustration. A real data set is also analyzed.
Fil: Boente Boente, Graciela Lina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Pires, Ana M.. Technical University of Lisbon; Portugal
Fil: Rodrigues, Isabel M.. Technical University of Lisbon; Portugal
Subject
Common principal components
Detection of outliers
Influence functions
Robust estimation
Estadística y Probabilidad
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:11336/15025