ALI SAID BARAKAT. A Nonparametric Multivariate Test For Homogeneity
Based on All Nearest Neighbors. (Under the direction of DANA
QUADE and IBRAHIM SALAMA.)
Schilling proposed a multivariate two-sample test using a fixed
number of nearest neighbors, and we cannot tell how many nearest
neighbors do we need to get the best results. In this research we
propose a test related to that proposed by Schilling. Our test uses all
nearest neighbors and it ",akes into account the position of each nearset
neighbor.
The exact properties of the test are studied as well as the
asymptotic ones. Also, as another proof, the nearest neighbors
technique has been used to prove the normality of the Wilcoxon-MannWhitney
statistic via the martingale central limit theorem.
Computer simulations are used to estimate the variance of the
test, and Monte Carlo simulation is used to compute its power.
For detecting location shift differences between two populations,
using Schilling's test, Hotelling's T2 test, and our test, we have found
that in many cases the proposed test compares favorably with
Hotelling's T2 test and in most cases it compares favorably with
Schilling's test.
Finally, using a subset of the Fisher iris data, the three tests are
used to test the hypothesis that the distribution ci the two sepal
measurements of the two species of iris are the same.

Title

Institute of Statistics Mimeo Series No. 1966 T. 1989, ASA Proceeding of the social statistics section, (1990), 222-225.

Publisher

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Publisher Country

Palestine

Publication Type

Both (Printed and Online)

Volume

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Year

1989

Pages

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