covrob_ogk: Robust Location and Scatter Estimation - Ortogonalized Gnanadesikan-Kettenring (OGK)

Description

Computes a robust multivariate location and scatter estimate with a high breakdown point, using the pairwise algorithm proposed by Marona and Zamar (2002) which in turn is based on the pairwise robust estimator proposed by Gnanadesikan-Kettenring (1972).

Usage

covrob_ogk(U, niter = 2, beta = 0.9)
dist_ogk(U, niter = 2, beta = 0.9)

Value

covrob_ogk(): list of robust estimates, $cov and $center.

dist_ogk(): vector of robust Mahalanobis (squared) distances.

Arguments

U: A matrix with no missing values and at least 2 columns.
niter: Number of number of iterations for the first step of the algorithm, usually 1 or 2 since iterations beyond the second do not lead to improvement.
beta: Coverage parameter for the final reweighted estimate. Default is 0.9.

References

Maronna, R.A. and Zamar, R.H. (2002) Robust estimates of location and dispersion of high-dimensional datasets; Technometrics 44(4), 307--317.

Yohai, R.A. and Zamar, R.H. (1998) High breakdown point estimates of regression by means of the minimization of efficient scale JASA 86, 403--413.

Gnanadesikan, R. and John R. Kettenring (1972) Robust estimates, residuals, and outlier detection with multiresponse data. Biometrics 28, 81--124.

Todorov V & Filzmoser P (2009), An Object Oriented Framework for Robust Multivariate Analysis. Journal of Statistical Software, 32(3), 1--47.

Examples

Run this code

X <- readRDS(system.file("testdata", "three-pops.rds", package = "bigutilsr"))
svd <- svds(scale(X), k = 5)

U <- svd$u
dist <- dist_ogk(U)
str(dist)