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

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概要

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• 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 bm,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.

• 日本統計学会の論文

著者

• Mukhopadhyay Nitis

  Department Of Statistics University Of Connecticut

• Chattopadhyay Bhargab

  Department of Statistics, U-4120, University of Connecticut

関連論文

• ON MP TEST AND THE MVUEs IN A N (θ,cθ) DISTRIBUTION WITH θ UNKNOWN : ILLUSTRATIONS AND APPLICATIONS
• Asymptotic Expansion of the Percentiles for a Sample Mean Standardized by GMD in a Normal Case with Applications
• ASYMPTOTIC EXPANSION OF THE PERCENTILES FOR A SAMPLE MEAN STANDARDIZED BY GMD IN A NORMAL CASE WITH APPLICATIONS

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