madmad {wavethresh}

Compute square of median absolute deviation (mad) function.

Description

This function simply returns the square of the median absolute deviation (mad) function in S-Plus. This is required for supply to the threshold series of functions which require estimates of spread on the variance scale (not the standard deviation scale).

Usage

madmad(x)

Arguments

x

The vector for which you wish to compute the square of mad on.

Value

The square of the median absolute deviation of the coefficients supplied by x.

RELEASE

Version 3.4.1 Copyright Guy Nason 1994

Note

Its a MAD MAD world!

Author(s)

G P Nason

See Also

threshold

Examples

#
#
# 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.