CONSTRUCTION AND COMPARISONS OF SIMULTANEOUS CONFIDENCEINTERVALS FOR THE MEAN DIFFERENCE OF MULTIVARIATE NORMALDISTRIBUTIONS

Xianhua MENG;Jinglong WANG;Xianyi WU

Journal of Systems Science & Complexity ›› 2010, Vol. 23 ›› Issue (2) : 303-314.

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Journal of Systems Science & Complexity ›› 2010, Vol. 23 ›› Issue (2) : 303-314. DOI: 10.1007/s11424-010-7058-4
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CONSTRUCTION AND COMPARISONS OF SIMULTANEOUS CONFIDENCEINTERVALS FOR THE MEAN DIFFERENCE OF MULTIVARIATE NORMALDISTRIBUTIONS

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Abstract

In this paper, Scheff\'{e} and Simplified Scheff\'{e}
simultaneous confidence intervals are first constructed for mean
difference of several multivariate normal distributions. Then the
authors theoretically prove that when there are only two
populations, Bonferroni bounds and Simplified Scheff\'{e} bounds are
the same and they are shorter than Scheff\'{e} bounds for p≤10.
In the case for 3≤k≤10 and 2≤p≤10, there exists
n(p,k) such that Bonferroni method is better than Simplified
Scheff\'{e} procedure for n≥n(p,k), otherwise Simplified
Scheff\'{e} procedure is better. Finally, the authors find out that
neither of Scheff\'{e} critical values nor Simplified Scheff\'{e}\
critical values\ are always larger than another through numerical
calculation.

Key words

Bonferroni simultaneous confidence interval / multiple comparison / Scheff\'{e} simultaneous confidence interval / simplified Scheff\'{e} simultaneous confidence interval.

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Xianhua MENG , Jinglong WANG , Xianyi WU. CONSTRUCTION AND COMPARISONS OF SIMULTANEOUS CONFIDENCEINTERVALS FOR THE MEAN DIFFERENCE OF MULTIVARIATE NORMALDISTRIBUTIONS. Journal of Systems Science and Complexity, 2010, 23(2): 303-314 https://doi.org/10.1007/s11424-010-7058-4
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