Geodesic
Multivariate multiple comparisons with a control in elliptical populations
Discussiones Mathematicae. Probability and Statistics, Tome 33 (2013) no. 1-2, pp. 191-205.

Voir la notice de l'article provenant de la source Library of Science

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.
Mots-clés : comparisons with a control, Bonferroni approximation and Monte Carlo simulation 
@article{DMPS_2013_33_1-2_a11,
     author = {Okamoto, Naoya and Seo, Takashi},
     title = {Multivariate multiple comparisons with a control in elliptical populations},
     journal = {Discussiones Mathematicae. Probability and Statistics},
     pages = {191--205},
     publisher = {mathdoc},
     volume = {33},
     number = {1-2},
     year = {2013},
     zbl = {1321.62060},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/DMPS_2013_33_1-2_a11/}
}
TY  - JOUR
AU  - Okamoto, Naoya
AU  - Seo, Takashi
TI  - Multivariate multiple comparisons with a control in elliptical populations
JO  - Discussiones Mathematicae. Probability and Statistics
PY  - 2013
SP  - 191
EP  - 205
VL  - 33
IS  - 1-2
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/DMPS_2013_33_1-2_a11/
LA  - en
ID  - DMPS_2013_33_1-2_a11
ER  - 
%0 Journal Article
%A Okamoto, Naoya
%A Seo, Takashi
%T Multivariate multiple comparisons with a control in elliptical populations
%J Discussiones Mathematicae. Probability and Statistics
%D 2013
%P 191-205
%V 33
%N 1-2
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/DMPS_2013_33_1-2_a11/
%G en
%F DMPS_2013_33_1-2_a11
Okamoto, Naoya; Seo, Takashi. Multivariate multiple comparisons with a control in elliptical populations. Discussiones Mathematicae. Probability and Statistics, Tome 33 (2013) no. 1-2, pp. 191-205. https://geodesic-test.mathdoc.fr/item/DMPS_2013_33_1-2_a11/

[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.

[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 .

[3] R.J. Muirhead, Aspects of Multivariate Statistical Theory (New York, Wiley, 1982). doi: 10.1002/9780470316559.

[4] N. Okamoto, A modified second order Bonferroni approximation in elliptical populations with unequal sample sizes, SUT Journal of Mathematics 41 (2005) 205-225.

[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.

[6] T. Seo, The effects of nonnormality on the upper percentiles of $T²_{max}$ statistic in elliptical distributions, Journal of the Japan Statistical Society 32 (2002) 57-76.

[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.