Multivariate multiple comparisons with a control in elliptical populations
Discussiones Mathematicae Probability and Statistics (2013)
- Volume: 33, Issue: 1-2, page 191-205
- ISSN: 1509-9423
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topNaoya Okamoto, and Takashi Seo. "Multivariate multiple comparisons with a control in elliptical populations." Discussiones Mathematicae Probability and Statistics 33.1-2 (2013): 191-205. <http://eudml.org/doc/270918>.
@article{NaoyaOkamoto2013,
abstract = {The approximate upper percentile of Hotelling's T²-type statistic is derived in order to construct simultaneous confidence intervals for comparisons with a control under elliptical populations with unequal sample sizes. Accuracy and conservativeness of Bonferroni approximations are evaluated via a Monte Carlo simulation study. Finally, we explain the real data analysis using procedures derived in this paper.},
author = {Naoya Okamoto, Takashi Seo},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {comparisons with a control; Bonferroni approximation and Monte Carlo simulation; Bonferroni approximation; Monte Carlo simulation},
language = {eng},
number = {1-2},
pages = {191-205},
title = {Multivariate multiple comparisons with a control in elliptical populations},
url = {http://eudml.org/doc/270918},
volume = {33},
year = {2013},
}
TY - JOUR
AU - Naoya Okamoto
AU - Takashi Seo
TI - Multivariate multiple comparisons with a control in elliptical populations
JO - Discussiones Mathematicae Probability and Statistics
PY - 2013
VL - 33
IS - 1-2
SP - 191
EP - 205
AB - The approximate upper percentile of Hotelling's T²-type statistic is derived in order to construct simultaneous confidence intervals for comparisons with a control under elliptical populations with unequal sample sizes. Accuracy and conservativeness of Bonferroni approximations are evaluated via a Monte Carlo simulation study. Finally, we explain the real data analysis using procedures derived in this paper.
LA - eng
KW - comparisons with a control; Bonferroni approximation and Monte Carlo simulation; Bonferroni approximation; Monte Carlo simulation
UR - http://eudml.org/doc/270918
ER -
References
top- [1] F. Bretz, M. Posch, E. Glimm, F. Klinglmueller, W. Maurer and K. Rohmeyer, Graphical approaches for multiple comparison procedures using weighted Bonferroni, Simes, or parametric tests, Biometrical Journal 53 (2011) No. 6, 894-913. doi: 10.1002/bimj.201000239. Zbl06043714
- [2] T. Iwashita, Asymptotic null and nonnull distribution of Hotelling's T²-statistic under the elliptical distribution, Journal of Statistical Planning and Inference 61 (1997) 85-104. doi: 10.1016/S0378-3758(96)00153-X . Zbl0879.62011
- [3] R.J. Muirhead, Aspects of Multivariate Statistical Theory (New York, Wiley, 1982). doi: 10.1002/9780470316559. Zbl0214.46506
- [4] N. Okamoto, A modified second order Bonferroni approximation in elliptical populations with unequal sample sizes, SUT Journal of Mathematics 41 (2005) 205-225. Zbl1092.62071
- [5] N. Okamoto and T. Seo, Pairwise multiple comparisons of mean vectors under elliptical populations with unequal sample sizes, Journal of the Japanese Society of Computational Statistics 17 (2004) 49-66. Zbl1261.62070
- [6] T. Seo, The effects of nonnormality on the upper percentiles of statistic in elliptical distributions, Journal of the Japan Statistical Society 32 (2002) 57-76. Zbl1044.62056
- [7] T. Seo and M. Toyama, On the estimation of kurtosis parameter in elliptical distributions, Journal of the Japan Statistical Society 26 (1996) 59-68. doi: 10.14490/jjss1995.26.59. Zbl0857.62054
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