Inferences on the common mean of several normal populations under heteroscedasticity

Original Paper
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Abstract

In this paper, we consider the problem of making inferences on the common mean of several normal populations when sample sizes and population variances are possibly unequal. We are mainly concerned with testing hypothesis and constructing confidence interval for the common normal mean. Several researchers have considered this problem and many methods have been proposed based on the asymptotic or approximation results, generalized inferences, and exact pivotal methods. In addition, Chang and Pal (Comput Stat Data Anal 53:321–333, 2008) proposed a parametric bootstrap (PB) approach for this problem based on the maximum likelihood estimators. We also propose a PB approach for making inferences on the common normal mean under heteroscedasticity. The advantages of our method are: (i) it is much simpler than the PB test proposed by Chang and Pal (Comput Stat Data Anal 53:321–333, 2008) since our test statistic is not based on the maximum likelihood estimators which do not have explicit forms, (ii) inverting the acceptance region of test yields a genuine confidence interval in contrast to some exact methods such as the Fisher’s method, (iii) it works well in terms of controlling the Type I error rate for small sample sizes and the large number of populations in contrast to Chang and Pal (Comput Stat Data Anal 53:321–333, 2008) method, (iv) finally, it has higher power than recommended methods such as the Fisher’s exact method.

Keywords

Common normal mean Genuine confidence interval Monte Carlo simulation Parametric bootstrap 

Notes

Acknowledgements

The authors would like to thank the referees for their constructive comments. The second author would like to acknowledge the Research Council of Shiraz University.

Supplementary material

180_2017_789_MOESM1_ESM.docx (14 kb)
Supplementary material 1 (docx 14 KB)
180_2017_789_MOESM2_ESM.docx (20 kb)
Supplementary material 2 (docx 20 KB)

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsK. N. Toosi University of TechnologyTehranIran
  2. 2.Department of StatisticsShiraz UniversityShirazIran

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