Sankhya: The Indian Journal of Statistics

2001, Volume 63, Series B, Pt. 3, pp. 286--297

NONPARAMETRIC ONE-SIDED TESTS FOR MULTIVARIATE DATA

By

HYO-IL PARK, *Chong-ju University*

JONG-HWA NA, *Chungbuk National University*

and

M.M. DESU, *State University of New York at Buffalo*

*SUMMARY.* We propose nonparametric one-sided test procedures for multivariate data. For small sample case,
we may obtain the exact null distribution by applying the permutation principle.
For large sample case, we consider the normal approximation for obtaining asymptotic tail probability or $p$-value.
We illustrate our procedures through an example. Then we discuss the consistency and asymptotic power of
our proposed test. Also we consider the cases when the directions of the unequal signs are reversed or
are alternating in the hypotheses. Finally, we compare the performances of our test with those of the test
based on the layer ranks through the empirical powers by computer simulations for some bivariate distributions.

*AMS (1991) subject classification.* Primary 62G10, 62H15.

*Key words and phrases.* Asymptotic power, consistency of test, median
test, permutation principle, Wilcoxon rank sum
test.