\HeaderA{madmad}{Compute square of median absolute deviation (mad) function.}{madmad}
\keyword{arith}{madmad}
\begin{Description}\relax
This function simply returns the square of the median absolute deviation (mad) function in S-Plus. This is required for supply to the \code{\LinkA{threshold}{threshold}} series of functions which require estimates of spread on the variance scale (not the standard deviation scale).
\end{Description}
\begin{Usage}
\begin{verbatim}
madmad(x)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{x}] The vector for which you wish to compute the square of mad on.
\end{ldescription}
\end{Arguments}
\begin{Value}
The square of the median absolute deviation of the coefficients supplied by \code{x}.
\end{Value}
\begin{Section}{RELEASE}
Version 3.4.1 Copyright Guy Nason 1994
\end{Section}
\begin{SeeAlso}\relax
\code{\LinkA{threshold}{threshold}}
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
#
#
# Generate some normal data with mean 0 and sd of 8
# and we'll also contaminate it with an outlier of 1000000
# This is akin to signal wavelet coefficients mixing with the noise.
#
#ContamNormalData <- c(1000000, rnorm(1000, mean=0, sd=8))
#
# What is the variance of the data?
#
#var(ContamNormalData)
# [1] 999000792
#
# Wow, a seriously unrobust answer!
#
# How about the median absolute deviation?
#
#mad(ContamNormalData)
# [1] 8.14832
# 
# A much better answer!
#
# Now let's use madmad to get the answer on the variance scale 
#
#madmad(ContamNormalData)
# [1] 66.39512
#
# The true variance was 64, so the 66.39512 was a much better answer
# than that returned by the call to the variance function.
\end{ExampleCode}
\end{Examples}

