A Distribution-Free Multivariate Sign Test Based on Interdirections
作者:
RonaldH. Randles,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1989)
卷期:
Volume 84,
issue 408
页码: 1045-1050
ISSN:0162-1459
年代: 1989
DOI:10.1080/01621459.1989.10478870
出版商: Taylor & Francis Group
关键词: Location test;One-sample multivariate location
数据来源: Taylor
摘要:
Distribution-free tests are investigated for the one-sample multivariate location problem. Counts, called interdirections, which measure the angular distance between two observation vectors relative to the positions of the other observations, are introduced. These counts are invariant under nonsingular linear transformations and have a small-sample distribution-free property over a broad class of population models, called distributions with elliptical directions, which includes all elliptically symmetric populations and many skewed populations. A sign test based on interdirections is described, including, as special cases, the two-sided univariate sign test and Blumen's bivariate sign test. The statistic is shown to have a limiting χ2pnull distribution and, because it is based on interdirections, it is also seen to be invariant and to have a small-sample distribution-free property. Pitman asymptotic relative efficiencies and a Monte Carlo study show the test to perform well compared with Hotelling'sT2, particularly when the underlying population is heavy-tailed or skewed. In addition, it consistently outperforms the component sign test, which is often recommended in the nonparametric literature.
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