Comparing Two Population Means and Variances: A Parametric Robust Way

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This article introduces a parametric robust way of comparing two population means and two population variances. With large samples the comparison of two means, under model misspecification, is lesser a problem, for, the validity of inference is protected by the central limit theorem. However, the assumption of normality is generally required, so that the inference for the ratio of two variances can be carried out by the familiar F statistic. A parametric robust approach that is insensitive to the distributional assumption will be proposed here. More specifically, it will be demonstrated that the normal likelihood function can be adjusted for asymptotically valid inferences for all underlying distributions with finite fourth moments. The normal likelihood function, on the other hand, is itself robust for the comparison of two means so that no adjustment is needed.

Original languageEnglish
Pages (from-to)2013-2029
Number of pages17
JournalCommunications in Statistics - Theory and Methods
Issue number10
StatePublished - Oct 2003


  • F test
  • Likelihood ratio test
  • Robust profile likelihood


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