scale estimation using the robust Qn estimator

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Description

Returns a scale estimation as calculated by the (robust) Qn estimator.

Usage

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qn(x, corrFact)

Arguments

x

a vector of data

corrFact

the finite sample bias correction factor. By default a value of ~ 2.219144 is used (assuming normality).

Details

The Qn estimator computes the first quartile of the pairwise absolute differences of all data values.

Value

The estimated scale of the data.

Warning

Earlier implementations used a wrong correction factor for the final result. Thus qn estimations computed with package pcaPP version > 1.8-1 differ about 0.12% from earlier estimations (version <= 1.8-1).

Note

See the vignette "Compiling pcaPP for Matlab" which comes with this package to compile and use this function in Matlab.

Author(s)

Heinrich Fritz, Peter Filzmoser <P.Filzmoser@tuwien.ac.at>

References

P.J. Rousseeuw, C. Croux (1993) Alternatives to the Median Absolute Deviation, JASA, 88, 1273-1283.

See Also

mad

Examples

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  # data with outliers
  x <- c(rnorm(100), rnorm(10, 10))
  qn(x)