Bahadur Efficiency of the Randomized Rank Statistics of Bell and Doksum.
Abstract
Bell and Doksum have introduced a class of statistics (T sub N)(H), called randomized rank statistics, as alternatives to a large class of two-sample linear rank statistics (S sub N)(H) and showed that the pitman asymptotic relative efficiency (ARE) of (T sub N)(H) with respect to (S sub N)(H) 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 N)(H) relative to (S sub N)(H) 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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1973
- Accession Number
- AD0766668
Entities
People
- Jayaram Sethuraman
- Robert P. Clickner
Organizations
- Florida State University