155
) observed in his Monte Carlo, that this, in some cases,
reduces the performance of the location statistic.
Now we consider the alternatives in which the bivariate
pairs were generated with location and scale differences
(pj = 0.5 and = 2.0, or p^ = 0.5 and = 3.0, or pj = 1*0
and = 3.0). For these alternatives, the statistics
corresponding to rows 7 and 8 are performing the best
overall. The statistics corresponding to rows 1 and 2 are
performing equivalently to rows 7 and 8, except for the
alternative where y^ = 0.5 and = 3.0 for the bivariate
Pearson VII distribution with v=3 and p=.2, and the
bivariate normal distribution with p-.2 or p=.5 This
possibly is reflecting the fact that CD performs slightly
better than the distribution-free scale statistic TM
nl >nc
when scale differences exist and, that, for this alternative
(i.e., p^= 0.5 and = 3.0) large scale differences
exist. As the correlation increases within any
distribution, we see that all the statistics are performing
moderately well and that for the last alternative where
Ui- 1.0 and = 3.0 when p=.5 or p=.8 no differences exist
between the ten statistics in general.
In summary, the recommended statistic is the quadratic
form which uses CD and the sample size (SS) weights for
TEn^ n (row 8). This statistic provides the best power in
general for the alternatives considered here. The statistic
corresponding to the quadratic form which uses CD and equal
weights for TEn n (row 7) performs for the most part
1 c