Robust Selection Procedures Based on Vector Ranks
OHIO STATE UNIV COLUMBUS DEPT OF STATISTICS
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We have studied mathematical properties of the vector rank procedure when applied to selecting the largest location parameter in randomized block models. Even if the data is not quantitative but ordinal, or is not from a location model but from a stochastically ordered family of distributions, the vector rank procedure is applicable. An important competing selection procedure is based on the robust estimate of location parameters Sen and Puri 1972. The selection procedure based on robust location estimates does not have the LFC difficulty that the vector rank procedure suffers from, and its relative efficiency compared to the means procedure is that of the Mann-Whitney-Wilcoxon test versus the t-test. A serious disadvantage, however, is that the robust location estimate method is not applicable if the data is ordinal or from a nonlocation family for example, see Lee and Dudewicz 1980 where the data is incomplete rank order scores or Lee 1980 where the distributional origin of the data is not known.
- Statistics and Probability