Multivariate Homogeneity Testing Using an Extended Concept of Nearest Neighbors
✍ Scribed by Ali S. Barakat; Dana Quade; Ibrahim A. Salama
- Publisher
- John Wiley and Sons
- Year
- 1996
- Tongue
- English
- Weight
- 413 KB
- Volume
- 38
- Category
- Article
- ISSN
- 0323-3847
No coin nor oath required. For personal study only.
✦ Synopsis
Given independent multivariate random samples (Xu: j = 1, ..., nil from 5, for i = 1,2, a test is desired for Ho: F1= F2 against general alternatives. Consider the k . (nl+ nz) possible ways of choosing one observation from the combined samples and then one of its k nearest neighbors. and let Sk be the proportion of these choices in which the point and neighbor are in the same sample. SCHILLING (1986) proposed s k as a test statistic, but did not indicate how to determine k. We suggest as test statistic W = N ks,, which we show is equivalent to a sum of N Wilcoxon rank sums, and also to a sum of two two-sample U-statistics of degrees (1.2) and (2, 1). Simulation with multiv~ate normal data suggests that our test is generally more powerful than Schilling's test using k = 1,2, or 3. We illustrate its use with Fisher's iris data.