Asymptotic Expansion of the Percentiles for a Sample Mean Standardized by GMD in a Normal Case with Applications

Abstract

This paper develops an asymptotic expansion of a percentile point of the Gini-based standardized sample mean. Such approximate percentiles can be used for proposing tests of hypotheses or confidence intervals of μ when samples arrive from a normal distribution with unknown mean μ and standard deviation σ. We have asymptotically expressed the percentile point b_m,α of the Gini-based pivot (1.5), that is, the Gini-based standardized sample mean. Using large-scale simulations, approximations, and data analyses, we report that the Gini-based test and confidence interval procedures for μ perform better or practically as well as the customarily employed Student's t-based procedures when samples arrive from a normal distribution with suspect outliers. This interesting finding is especially noteworthy when we have a small random sample from a normal population with possible outliers.