Guarded Weights of Evidence and Acceptability Profiles Based on Signs: II. Asymptotic Results

The concepts of guarded weights of evidence and acceptability profiles have been extended to the distribution-free setting in Dollinger, Kulinskaya & Staudte (1999). In that first of two parts the advantages of these concepts relative to traditional ones such as p -values and confidence intervals derived from hypothesis tests are emphasized for small samples. Here in Part II asymptotic expressions are found for guarded weights of evidence for hypothesesregarding the median of a symmetric distribution and related acceptability profiles for the median. It is also seen that for local alternatives the efficacy and Pitman asymptotic relative efficiency of the sign statistic for testing hypotheses carries over to the more general setting of guarded weights of evidence.