Some admissible nonparametric tests and a minimal complete class theorem
Seung-Chun Li · 1990
The purpose of this dissertation is to demonstrate the admissibility of some well-known nonparametric tests. It is found that many standard nonparametric tests, such as Mann-Whitney-Wilcoxon test, Fisher-Yates test, Savage test, and median test, which are linear rank tests, are admissible for the two-sample nonparametric testing problem. It turns out that the admissibility of a linear rank test depends on the regression constants not the scores. We also prove that Kruskal-Wallis test is admissible for the one-way layout testing problem;This dissertation is also concerned with finding minimal complete class of statistical decision problems. A new mechanism, called extended stepwise Bayes technique which is a general version of the stepwise Bayes technique, is developed. When the parameter space [theta] is finite and the risk set is closed and bounded from below, a minimal complete class is given using the extended stepwise Bayes technique.