where
1 if t>0
'i'(t)
0 if t < 0 ,
which is Kendall's Tau applied to the transformed
observations. He noted that tt is neither distribution-free
nor asymptotically distribution-free in this setting and
thus recommended a permutation test which is conditionally
distribution-free based on tt for small samples. This
permutation test was based on conditioning on what he called
/
the collection matrix, Cn,
He noted that under HQ and conditional on Cn, there are 2n
equally likely transformed samples possible,
each being determined by a different collection of T* 's
j|f
where ¥^ = {1 or -1}. For larger samples, he obtains the
asymptotic distribution which can be used to approximate the
permutation test.
One nice property of the statistic tt which Kepner
notes, is that tt is insensitive to unequal marginal