Multivariate multiple comparisons with a control in elliptical populations

• Autorzy: Naoya Okamoto , Takashi Seo
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

comparisons with a control; Bonferroni approximation and Monte Carlo simulation

Kategorie tematyczne

• 65C05: Monte Carlo methods
• 62H10: Distribution of statistics
• 60E05: Distributions: general theory

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae Probability and Statistics
• Rocznik: 2013
• Tom: 33
• Numer: 1-2
• Strony: 191-205

Daty

wydano

2013

otrzymano

2013-09-18

poprawiono

2013-11-18

Twórcy

autor

Naoya Okamoto

• Department of Food Sciences, Tokyo Seiei College 1-4-6, Nishishinkoiwa, Katsushika-ku, Tokyo 124-8530 Japan

autor

Takashi Seo

• Department of Mathematical Information Science, Tokyo University of Science 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan

Bibliografia

• [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.

Identyfikatory

DOI

10.7151/dmps1152