Sn function

Robust Location-Free Scale Estimate More Efficient than MAD

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

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

s_Sn(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.
• na.rm: logical specifying if missing values (NA) should be removed from x before further computation. If false as by default, and if there are NAs, i.e., if(anyNA(x)), the result will be NA.
• mu.too: logical indicating if the median(x) should also be returned for s_Sn().
• ...: potentially further arguments for s_Sn() passed to Sn().

Returns

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

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

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.

See Also

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

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

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)

(s <- Sn(c(1:4, 10, Inf, NA), na.rm=TRUE))
stopifnot(is.finite(s), all.equal(3.5527554, s, tol=1e-10))