文章基本信息

标题：Asymptotic Expansion of the Percentiles for a Sample Mean Standardized by GMD in a Normal Case with Applications
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作者：Nitis Mukhopadhyay ; Bhargab Chattopadhyay
期刊名称：JOURNAL OF THE JAPAN STATISTICAL SOCIETY
印刷版ISSN：1882-2754
电子版ISSN：1348-6365
出版年度：2012
卷号：42
期号：2
页码：165-184
DOI：10.14490/jjss.42.165
出版社：JAPAN STATISTICAL SOCIETY
摘要：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.
关键词：Cornish-Fisher expansion;Gini's mean difference;normalized sample mean;outlier;robustness;suspect outlier;taylor expansion