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T^2 Type Test Statistic and Simultaneous Confidence Intervals for Two Sub-mean Vectors

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  • Tamae Kawasaki
  • Toshiki Naito
  • Takashi Seo

Abstract

In this paper, we consider tests for sub-mean vectors and its simultaneous confidence intervals in two-sample problems. We give the T^2 type test statistic and the simultaneous confidence intervals by using two approximate upper percentiles of T^2 type test statistic. One of the approximate percentiles is obtained by normal approximation for a part of the T^2 type statistic, and the other is an approximation obtained by correcting the degrees of freedom of the F distribution. Finally, we investigate the asymptotic behavior of the approximate upper percentiles of T^2 type statistic by Monte Carlo simulation, and we give an example to illustrate the simultaneous confidence intervals.

Suggested Citation

  • Tamae Kawasaki & Toshiki Naito & Takashi Seo, 2020. "T^2 Type Test Statistic and Simultaneous Confidence Intervals for Two Sub-mean Vectors," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 9(1), pages 1-1, January.
    • Handle: RePEc:ibn:ijspjl:v:9:y:2020:i:1:p:1
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    References listed on IDEAS

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    1. Gupta, Arjun K. & Xu, Jin & Fujikoshi, Yasunori, 2006. "An asymptotic expansion of the distribution of Rao's U-statistic under a general condition," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 492-513, February.
    2. Provost, Serge B., 1990. "Estimators for the parameters of a multivariate normal random vector with incomplete data on two subvectors and test of independence," Computational Statistics & Data Analysis, Elsevier, vol. 9(1), pages 37-46, January.
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    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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