Robust Location-Free Scale Estimate More Efficient than MAD

Compute the robust scale estimator \(S_n\), 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().

Value

Sn() returns a number, the \(S_n\) 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.

Author

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)
#> [1] 11.2671
Sn(x, c=1)# 9
#> [1] 9
Sn(x[1:18], c=1)# 9
#> [1] 9
set.seed(153)
x <- sort(c(rnorm(80), rt(20, df = 1)))
s_Sn(x, mu.too=TRUE)
#> [1] -0.2154659  1.1127858

(s <- Sn(c(1:4, 10, Inf, NA), na.rm=TRUE))
#> [1] 3.552755
stopifnot(is.finite(s), all.equal(3.5527554, s, tol=1e-10))