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

Source: R/OGK.R

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).

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

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

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.

Value

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

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

Details

The method proposed by Marona and Zamar (2002) allowes to obtain positive-definite and almost affine equivariant robust scatter matrices starting from any pairwise robust scatter matrix. The default robust estimate of covariance between two random vectors used is the one proposed by Gnanadesikan and Kettenring (1972) but the user can choose any other method by redefining the function in slot vrob of the control object CovControlOgk. Similarly, the function for computing the robust univariate location and dispersion used is the tau scale defined in Yohai and Zamar (1998) but it can be redefined in the control object.

The estimates obtained by the OGK method, similarly as in CovMcd are returned as 'raw' estimates. To improve the estimates a reweighting step is performed using the coverage parameter beta and these reweighted estimates are returned as 'final' estimates.

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. doi:10.18637/jss.v032.i03.

Examples

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)
#>  num [1:517] 9.56 9.66 3.51 4.16 7.81 ...