synlik (version 0.1.6)

robCov: Robust covariance matrix estimation

Description

Obtains a robust estimate of the covariance matrix of a sample of multivariate data, using Campbell's (1980) method as described on p231-235 of Krzanowski (1988).

Usage

robCov(sY, alpha = 2, beta = 1.25)

Value

A list where:

• Ea square root of the inverse covariance matrix. i.e. the inverse cov matrix is t(E)%*%E;

• half.ldet.VHalf the log of the determinant of the covariance matrix;

• mYThe estimated mean;

• sdThe estimated standard deviations of each variable.

Arguments

sY

A matrix, where each column is a replicate observation on a multivariate r.v.

alpha

tuning parameter, see details.

beta

tuning parameter, see details.

Author

Simon N. Wood, maintained by Matteo Fasiolo <[e-mail]>.

Details

Campbell (1980) suggests an estimator of the covariance matrix which downweights observations at more than some Mahalanobis distance d.0 from the mean. d.0 is sqrt(nrow(sY))+alpha/sqrt(2). Weights are one for observations with Mahalanobis distance, d, less than d.0. Otherwise weights are d.0*exp(-.5*(d-d.0)^2/beta)/d. The defaults are as recommended by Campbell. This routine also uses pre-conditioning to ensure good scaling and stable numerical calculations.

References

Krzanowski, W.J. (1988) Principles of Multivariate Analysis. Oxford. Campbell, N.A. (1980) Robust procedures in multivariate analysis I: robust covariance estimation. JRSSC 29, 231-237.

Examples

p <- 5;n <- 100
Y <- matrix(runif(p*n),p,n)
robCov(Y)