number by which the result is multiplied; the default
achieves consistency for normally distributed data. Note that until
Nov. 2010, “thanks” to a typo in the very first papers, a slightly
wrong default constant, 2.2219, was used instead of the correct one
which is equal to 1 / (sqrt(2) * qnorm(5/8)) (as mentioned
already on p.1277, after (3.7) in Rousseeuw and Croux (1993)).
If you need the old slightly off version for historical
reproducibility, you can use Qn.old().
Note that the relative difference is only about 1 in 1000, and that
the correction should not affect the finite sample corrections for
n <= 9.
finite.corr
logical indicating if the finite sample bias
correction factor should be applied. Defaults 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().
Details
As the (default, consistency) constant needed to be corrected,
the finite sample correction has been based on a much more extensive
simulation, and on a 3rd or 4th degree polynomial model in 1/n
for odd or even n, respectively.
Value
Qn() returns a number, the Qn robust scale
estimator, scaled to be consistent for σ^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
(μ) and scale; this is typically only useful for
covOGK(*, sigmamu = s_Qn).
Rousseeuw, P.J. and Croux, C. (1993)
Alternatives to the Median Absolute Deviation,
Journal of the American Statistical Association88, 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; available via Springer Link.
About the typo in the constant:
Christophe Croux (2010)
Private e-mail, Fri Jul 16, w/ Subject
Re: Slight inaccuracy of Qn implementation .......
See Also
mad for the ‘most robust’ but much less efficient
scale estimator; Sn for a similar faster but less
efficient alternative. Finally, scaleTau2 which some
consider “uniformly” better than Qn or competitors.