Two-sample rank tests with truncated populations |
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Authors: | C H Lin Shashikala Sukhatme |
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Institution: | (1) Ming Chuan College, Taipei, ROC;(2) Department of Statistics, Iowa State University, 50011 Ames, IA |
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Abstract: | LetX
1,…,X
m
andY
1,…,Y
n
be two independent samples from continuous distributionsF andG respectively. Using a Hoeffding (1951) type theorem, we obtain the distributions of the vector S=(S
(1),…,S
(n)), whereS
(j)=# (X
i
’s≤Y
(j)) andY
(j) is thej-th order statistic ofY sample, under three truncation models: (a)G is a left truncation ofF orG is a right truncation ofF, (b)F is a right truncation ofH andG is a left truncation ofH, whereH is some continuous distribution function, (c)G is a two tail truncation ofF. Exploiting the relation between S and the vectorR of the ranks of the order statistics of theY-sample in the pooled sample, we can obtain exact distributions of many rank tests. We use these to compare powers of the
Hajek test (Hajek 1967), the Sidak Vondracek test (1957) and the Mann-Whitney-Wilcoxon test.
We derive some order relations between the values of the probagility-functions under each model. Hence find that the tests
based onS
(1) andS
(n) are the UMP rank tests for the alternative (a). We also find LMP rank tests under the alternatives (b) and (c). |
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Keywords: | Hoeffding type theorem UMP rank test LMP rank test |
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