ABSTRACT
Hendriks and Landsman (1998) [154] developed asymptotic test statistics for
the equality of two extrinsic means on a submanifoldM of the Euclidean space RD, based on independent samples drawn from the two distributions. Using a general local orthonormal frame field methodology, developed in Patrangenaru
(1998) [266], and in Bhattacharya and Patrangenaru (2005) [43], one may find
an alternate two sample test statistic for the equality of two extrinsic means.
Such an approach is due to A. Bhattacharya (2008) [25], who tested the equal-
ity of mean extrinsic objects by taking the pooled extrinsic sample mean as an
estimator of the hypothesized extrinsic mean in two correlated pairs (or not)
of objects on a manifold embedded in the Euclidean space; note that this test
statistic can not be extended to matched pairs, since it is derived from the a
test for the equality of two extrinsic means, by pooling without pairing the
observations measured for each individual.
