cov.ogk: Ortogonalized Gnanadesikan-Kettenring (OGK) Robust...
In abnormally-distributed/cvreg: Cross Validation and Robust Estimation Utilities

Description Usage Arguments Value References

Computes a robust covariance and location estimator using the pairwise algorithm proposed by Marona and Zamar (2002), which solves the problem concerning the lack of affine equivariance in the method proposed by Gnanadesikan-Kettenring (1972). Furthermore, the OGK estimator is guaranteed to return a positive-definite covariance matrix when n > p. In the implementation in this package, when n < p, mild shrinkage is applied to induce a positive-definite matrix.

Several options to use as scale and location estimators are offered here:

- "tau" is the tau-scale defined in Yohai and Zamar (1998).
- "pb" is the percentage bend estimator (Shoemaker & Hettmansperger, 1982).
- "bisq" is Tukey's bisquare estimator.
- "huber" is Huber's psi estimator (Huber, 1964).
- "mopt" is the modified optimal estimator.
- "Qn" and "Sn" are two alternatives to the median based measures of location and scale (Rousseeuw, Peter, & Croux, 1993).

cov.ogk(
  x,
  method = c("tau", "pb", "bisq", "huber", "mopt", "Qn", "Sn"),
  iter = 2,
  opts = list(b = 0.1, eff = 0.9)
)

`x`	a data frame or matrix of numeric covariates
`method`	"tau", "pb", "bisq", "huber", "mopt", "Qn", "Sn"
`iter`	the number of refinement steps. defaults to 2. can be 0 if the raw ogk estimator is desired.
`opts`	list of options for the various scale estimators. "b" determines the percentage bend coefficient for "pb", "eff" determines the efficiency of the "huber", "bisquare" and "mopt" scale estimators.

a covRobust object containing the following elements:

center: multivariate mean of cleaned data set after removing outliers.
cov: covariance matrix of cleaned data set after removing outliers.
dist: the mahalanobis distances used in calculating the weights.
outliers: the indices of the outliers identified.
weights: the weights for downweighting outliers.

Huber, P. J. (1964). Robust estimation of a location parameter. Ann. Math. Statist. 35, 73–101.

Shoemaker, L. H., & Hettmansperger, T. P. (1982). Robust estimates and tests for the one- and two-sample scale models. Biometrika, 69:47–54

Rousseeuw, Peter J.; Croux, Christophe (1993), Alternatives to the Median Absolute Deviation. Journal of the American Statistical Association, 88(424): 1273–1283, doi:10.2307/229126

Yohai, R.A. and Zamar, R.H. (1998) High breakdown point estimates of regression by means of the minimization of efficient scale. Journal of the American Statistical Association, 86:403–413.

abnormally-distributed/cvreg documentation built on May 3, 2020, 3:45 p.m.