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Inferences on the common mean of several normal populations under heteroscedasticity

Author

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  • Ahad Malekzadeh

    () (K. N. Toosi University of Technology)

  • Mahmood Kharrati-Kopaei

    () (Shiraz University)

Abstract

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.

Suggested Citation

  • Ahad Malekzadeh & Mahmood Kharrati-Kopaei, 2018. "Inferences on the common mean of several normal populations under heteroscedasticity," Computational Statistics, Springer, vol. 33(3), pages 1367-1384, September.
  • Handle: RePEc:spr:compst:v:33:y:2018:i:3:d:10.1007_s00180-017-0789-0
    DOI: 10.1007/s00180-017-0789-0
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    References listed on IDEAS

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    1. repec:bla:jorssb:v:79:y:2017:i:5:p:1601-1618 is not listed on IDEAS
    2. K. Krishnamoorthy & Yong Lu, 2003. "Inferences on the Common Mean of Several Normal Populations Based on the Generalized Variable Method," Biometrics, The International Biometric Society, vol. 59(2), pages 237-247, June.
    3. Hannig, Jan & Iyer, Hari & Patterson, Paul, 2006. "Fiducial Generalized Confidence Intervals," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 254-269, March.
    4. Chang, Ching-Hui & Pal, Nabendu, 2008. "Testing on the common mean of several normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 321-333, December.
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