scaleunit_ function(S)
{

# Scale a data set so that the presumption of unit variance for
# the mixture components is tenable.  This can be done prior to
# invocation of  normal.S, so that the tests performed therein
# are meaningful. 
#
# Required Input:
# 	S  is a vector of data
#
# Outputs:
# 	S  is a vector of scaled data

S_ S-mean(S)
n_ length(S)

# Suppose S_i ~ Normal(0, sigma^2).  One could estimate sigma by
# the sample standard deviation of the S_i and scale the data
# accordingly.  The problem with doing this is that, in the
# presence of heterogeneity, the overall variance is calibrated
# to 1; we really want the mixture components to have unit
# variance.  A better option is to scale by a different estimate 
# of sigma.  Noting that Var(S_i^2) = 2 sigma^4, we can estimate 
# sigma by the fourth root of one-half the sample variance of the 
# squared observations.  In the presence of heterogeneity, the 
# overall variance can then be calibrated to something more than 1.

SS_ S^2
sig_ (((sum(SS^2)-sum(SS)^2/n)/(n-1))/2)^.25

S_ S/sig 

return(S)
result
}