robustbase (version 0.5-0-1)

Qn: Robust Location-Free Scale Estimate More Efficient than MAD

Description

Compute the robust scale estimator $Q_n$, an efficient alternative to the MAD.

Usage

Qn(x, constant = 2.2219, finite.corr = missing(constant))
s_Qn(x, mu.too = FALSE, ...)

Arguments

x

numeric vector of observations.

constant

number by which the result is multiplied; the default achieves consisteny for normally distributed data.

finite.corr

logical indicating if the finite sample bias correction factor should be applied. Default to TRUE unless constant is specified.

mu.too

logical indicating if the median(x) should also be returned for s_Qn().

...

potentially further arguments for s_Qn() passed to Qn().

Value

• Qn() returns a number, the $Q_n$ robust scale estimator, scaled to be consistent for $\sigma^2$ and i.i.d. Gaussian observatsions, optionally bias corrected for finite samples.

  s_Qn(x, mu.too=TRUE) returns a length-2 vector with location ($\mu$) and scale; this is typically only useful for covOGK(*, sigmamu = s_Qn).

Details

............ FIXME ........

References

Rousseeuw, P.J. and Croux, C. (1993) Alternatives to the Median Absolute Deviation, Journal of the American Statistical Association 88, 1273--1283.

Christophe Croux and Peter J. Rousseeuw (1992) Time-Efficient Algorithms for Two Highly Robust Estimators of Scale, Computational Statistics, Vol. 1, ed. Dodge and Whittaker, Physica-Verlag Heidelberg, 411--428; also available from http://win-www.uia.ac.be/u/statis/abstract/Timeff92.htm.

See Also

mad for the most robust but much less efficient scale estimator; Sn for a similar faster but less efficient alternative; scaleTau2.

Examples

set.seed(153)
x <- sort(c(rnorm(80), rt(20, df = 1)))
s_Qn(x, mu.too = TRUE)
Qn(x, finite.corr = FALSE)