arw {StatDA} | R Documentation

## Adaptive reweighted estimator for multivariate location and scatter

### Description

Adaptive reweighted estimator for multivariate location and scatter with hard-rejection weights. The multivariate outliers are defined according to the supremum of the difference between the empirical distribution function of the robust Mahalanobis distance and the theoretical distribution function.

### Usage

    arw(x, m0, c0, alpha, pcrit)

### Arguments

`x` | Dataset (n x p)
`m0` | Initial location estimator (1 x p)
`c0` | Initial scatter estimator (p x p)
`alpha` | Maximum thresholding proportion (optional scalar, default: alpha = 0.025)
`pcrit` | Critical value obtained by simulations (optional scalar, default value obtained from simulations)

### Details

At the basis of initial estimators of location and scatter, the function arw performs a reweighting step to adjust the threshold for outlier rejection. The critical value pcrit was obtained by simulations using the MCD estimator as initial robust covariance estimator. If a different estimator is used, pcrit should be changed and computed by simulations for the specific dimensions of the data x.

### Value

`m` | Adaptive location estimator (p x 1)
`c` | Adaptive scatter estimator (p x p)
`cn` | Adaptive threshold ("adjusted quantile")
`w` | Weight vector (n x 1)

### Author(s)

Moritz Gschwandtner <e0125439@student.tuwien.ac.at>
Peter Filzmoser <P.Filzmoser@tuwien.ac.at> http://www.statistik.tuwien.ac.at/public/filz/

### References

P. Filzmoser, R.G. Garrett, and C. Reimann (2005). Multivariate outlier detection in exploration geochemistry. Computers & Geosciences.

### Examples

    x <- cbind(rnorm(100), rnorm(100))
    arw(x, apply(x,2,mean), cov(x))

[Package StatDA version 1.0 Index]