1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
|
\name{Sn}
\alias{Sn}
\alias{s_Sn}
%
\title{Robust Location-Free Scale Estimate More Efficient than MAD}
\description{
Compute the robust scale estimator \eqn{S_n}{Sn}, an efficient
alternative to the MAD.
}
\usage{
Sn(x, constant = 1.1926, finite.corr = missing(constant), na.rm = FALSE)
s_Sn(x, mu.too = FALSE, \dots)
}
\arguments{
\item{x}{numeric vector of observations.}
\item{constant}{number by which the result is multiplied; the default
achieves consisteny for normally distributed data.}
\item{finite.corr}{logical indicating if the finite sample bias
correction factor should be applied. Default to \code{TRUE} unless
\code{constant} is specified.}
\item{na.rm}{logical specifying if missing values (\code{\link{NA}})
should be removed from \code{x} before further computation. If false
as by default, and if there are \code{NA}s, i.e., \code{if(anyNA(x))},
the result will be \code{NA}.}
\item{mu.too}{logical indicating if the \code{\link[stats]{median}(x)} should
also be returned for \code{s_Sn()}.}
\item{\dots}{potentially further arguments for \code{s_Sn()} passed to
\code{Sn()}.}
}
\value{
\code{Sn()} returns a number, the \eqn{S_n}{Sn} robust scale estimator, scaled to be
consistent for \eqn{\sigma^2} and i.i.d. Gaussian observations,
optionally bias corrected for finite samples.
\code{s_Sn(x, mu.too=TRUE)} returns a length-2 vector with location
(\eqn{\mu}) and scale; this is typically only useful for
\code{\link{covOGK}(*, sigmamu = s_Sn)}.
}
\details{
............ FIXME ........
}
\references{
Rousseeuw, P.J. and Croux, C. (1993)
Alternatives to the Median Absolute Deviation,
\emph{Journal of the American Statistical Association} \bold{88}, 1273--1283.
}
\seealso{\code{\link[stats]{mad}} for the \sQuote{most robust} but much
less efficient scale estimator;
\code{\link{Qn}} for a similar more efficient but slower alternative;
\code{\link{scaleTau2}}.
}
\author{Original Fortran code:
Christophe Croux and Peter Rousseeuw \email{rousse@wins.uia.ac.be}.
\cr
Port to C and R: Martin Maechler, \email{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))
}
\keyword{robust}
\keyword{univar}
|
