For vectors, Sn(X) is the scale estimator of the elements in X. For
matrices, Sn(X) is a row vector containing the scale estimator value of
each column. For 3D arrays, Sn(X) is the robust scale estimator of the
elements along the first non-singleton dimension of X.
Sn(X,dim) takes the robust estimator along the dimension dim of X.
, i=1,2, ...n, j=1, 2, ..., n.
For each i we compute the median of |x_i-x_j|, j=1, 2, ..., n.
This yields n numbers, the median of which gives the final estimate of
S_n. This estimator is the robust version of Gini's average difference,
which one would obtain when replacing medians by averages
More in detail Sn = cn \times c \times lomed_i { highmed_j
|x_i-x_j|}, i=1,2, ...n, j=1, 2, ..., n, where lomed (low
median) is [(n+1)/2]-th order statistic out of n numbers) and
himed (high median) is the ([n/2]+1)-th order statistic out of the
n numbers. c is the so called asymptotic consistency factor and is
equal to 1.1926 while cn is a finite sample correction factor to make
the estimator unbiased.