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Abstract
We present the FRB package for R, which implements the fast and robust bootstrap. This method constitutes an alternative to ordinary bootstrap or asymptotic inference procedures when using robust estimators such as S-, MM- or GS-estimators. The package considers three multivariate settings: principal components analysis, Hotelling tests and multivariate regression. It provides both the robust point estimates and uncertainty measures based on the fast and robust bootstrap. In this paper we give some background on the method, discuss the implementation and provide various examples.
Highlights
In this paper we introduce the FRB package for R (R Core Team 2012) which implements robust multivariate data analysis with inference based on the fast and robust bootstrap (FRB) method of Salibian-Barrera and Zamar (2002)
In order to obtain statistical procedures which are more resistant to outliers, it generally suffices to replace the classical estimates by robust estimates such as the ones described above, as briefly explained
In this paper we provided some background on the fast and robust bootstrap method and we introduced the R package FRB for robust multivariate inference
Summary
In this paper we introduce the FRB package for R (R Core Team 2012) which implements robust multivariate data analysis with inference based on the fast and robust bootstrap (FRB) method of Salibian-Barrera and Zamar (2002). The settings have in common that the classical analysis methods are robustified by the use of multivariate robust estimates of the type of S-, MM- or GS-estimates. These specific estimates allow the FRB to be applied in order to extend the robust point estimates with accompanying standard errors, confidence intervals or p values. Principal components analysis aims to explain the covariance structure of G. It can be used to reduce the dimension of the data without too much loss of information, by projecting the observations onto a small number of principal components which are linear combinations of the original p variables. In classical PCA, the components are estimated by the eigenvectors of the sample covariance or shape matrix. The corresponding eigenvalues measure the amount of variance explained by the components
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