OutlierStatistic: Nonparametric Outlier Statistic
In probout: Unsupervised Multivariate Outlier Probabilities for Large Datasets

Description Usage Arguments Value References Note See Also Examples

View source: R/OutlierStatistic.R

Robust nonparametric outlier statistic for univariate or multivariate data.

1	OutlierStatistic( x, nproj=1000, prior=NULL, seed=NULL)

`x`	A numeric vector or matrix for which the outlier statistic is to be determined.
`nproj`	If `x` is multivariate, the number of random projections to be used in computing the statistic.
`prior`	If `x` is multivariate, a prior estimate of the statistic for each observation in `x`, to be used as a base line for maximization relative to new random projections.
`seed`	An optional integer argument to `set.seed` for reproducible simulations. By default the current seed will be used. Reproducibility can also be achieved by calling `set.seed` before calling `OutlierStatistic`.

A vector giving the maximum value of the outlier statistic for each observation over all projections.

W. A. Stahel, Breakdown of Covariance Estimators, doctoral thesis, Fachgruppe Fur Statistik, Eidgenossische Technische Hochshule (ETH), 1981.

D. L. Donoho, Breakdown Properties of Multivariate Location Estimators, doctoral thesis, Department of Statistics, Harvard University, 1982.

Note that partition probabilities are computed from an exponential distribution fit to the outlier statistic, rather than from the empirical distribution of the outlier statistic.

partProb

 stat <- OutlierStatistic(faithful)
 q.99 <- quantile(stat,.99)
 out <- stat > q.99

 plot( faithful[,1], faithful[,2], 
       main="red : .99 quantile for outlier statistic", cex=.5)
 points( faithful[out,1], faithful[out,2], 
         pch = 4, col = "red", lwd = 1, cex = .5)

 require(mvtnorm)

 set.seed(0)
 Sigma <- crossprod(matrix(rnorm(2*2),2,2))
 x <- rmvt( 10000, sigma = Sigma, df = 2) 

 stat <- OutlierStatistic(x)
 q.95 <- quantile(stat,.95)

 hist(x, main = "gray : .95 quantile for outlier statistic", col = "black")
 abline( v = x[stat > q.95], col = "gray")
 hist(x, col = "black", add = TRUE)