# robCov: Robust covariance matrix estimation In synlik: Synthetic Likelihood methods for intractable likelihoods.

## 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

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

## 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.

## 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.

## Value

A list where:

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

• `half.ldet.V`Half the log of the determinant of the covariance matrix;

• `mY`The estimated mean;

• `sd`The estimated standard deviations of each variable.

## Author(s)

Simon N. Wood, maintained by Matteo Fasiolo <[email protected]>.

## 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

 ```1 2 3``` ```p <- 5;n <- 100 Y <- matrix(runif(p*n),p,n) robCov(Y) ```

synlik documentation built on May 29, 2017, 12:16 p.m.