134
5.2 Monte Carlo for the Scale Test
In this section, nine statistics will be investigated
to compare their performance under the null and alternative
hypotheses. Three of the nine, are versions of the CD
statistic, where each version uses a different estimator for
the variance of CD (Section 2.4). The next three statistics
are members of the class of statistics proposed in Section
3.2, where the common location parameter was known, while
the following three are members of the class of statistics
proposed in Section 3.3, where the common location parameter
was unknown and thus estimated. Table 5.1 summarizes the
nine statistics considered in this Monte Carlo.
In this Monte Carlo three bivariate distributions (each
with common location (0,0)) were considered for generating
/
the bivariate samples. Although, generally the common
location is not (0,0), it was used without loss of
generality. The first distribution, the bivariate normal,
was generated using the subroutine GGNSM of the
International Mathematical and Statistical Library (IMSL).
It allows specification of the variance-covarianee structure
for the bivariate pairs. The remaining two distributions
were generated using a technique for generating elliptically
symmetric distributions proposed in Johnson and Ramberg
(1977). The two distributions are both Pearson Type VII
multivariate distributions which were generated in the
following manner. For a sample of size n, 2n uniform [0,1]