Bahadur Efficiency of the Randomized Rank Statistics of Bell and Doksum.
FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS
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Bell and Doksum have introduced a class of statistics T sub NH, called randomized rank statistics, as alternatives to a large class of two-sample linear rank statistics S sub NH and showed that the pitman asymptotic relative efficiency ARE of T sub NH with respect to S sub NH is unity. The tests based on the randomized rank tests have been subject to much criticism, but all these criticisms seem to relate to poor performances in finite samples. It is shown that the Bahadur Asymptotic relative efficiency of T sub NH relative to S sub NH is less than one, under mild regularity conditions. When normal scores are used, the Bahadur ARE is shown to decrease as the alternative recedes from the null hypothesis. The same phenomenon is illustrated by analytic methods and numerical computations in some other situations. Author
- Statistics and Probability