Confidence intervals which admit positively (semi) relevent sursets that are not invariant

Abstract

Let be a random sample from a normal population with unknown mean μ and variance σ². L. Brown has shown that the standard confidence interval for μ (depending on the sample mean [Xbar] and sample variance S² admits a positively relevant subset. R Olshen has generalized these results to cover confidence ellipsoids. The positively (semi) relevant subsets demonstrated in both cases are invariant with respect to σ² This paper demonstrates that events the form

(where Y is independent of [Xbar] and S²) are positively biased semirelevant subsets for the standard confidence interval for μ but are not invariant with respect to σS².

Keywords:

• Confidence Intervals
• Positive Semirelevant subsets
• Negative Semirelevant subsets