Robust Location-Free Scale Estimate More Efficient than MAD

Description

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

Usage

Sn(x, constant = 1.1926, finite.corr = missing(constant))

s_Sn(x, mu.too = FALSE, ...)

Arguments

Details

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

Value

Sn() returns a number, the Sn robust scale estimator, scaled to be consistent for σ^2 and i.i.d. Gaussian observatsions, optionally bias corrected for finite samples.

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

Author(s)

Original Fortran code: Christophe Croux and Peter Rousseeuw rousse@wins.uia.ac.be.
Port to C and R: Martin Maechler, maechler@R-project.org

References

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

See Also

mad for the ‘most robust’ but much less efficient scale estimator; Qn for a similar more efficient but slower alternative; scaleTau2.

Examples

x <- c(1:10, 100+1:9)# 9 outliers out of 19
Sn(x)
Sn(x, c=1)# 9
Sn(x[1:18], c=1)# 9
set.seed(153)
x <- sort(c(rnorm(80), rt(20, df = 1)))
s_Sn(x, mu.too=TRUE)

Results