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On minimum volume properties of some confidence regions for multiple multivariate normal means

Author

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  • Bedbur, S.
  • Lennartz, J.M.
  • Kamps, U.

Abstract

In a multi-sample model of multivariate normal distributions with covariance matrices being known or known except for unknown multipliers, simultaneous confidence regions for the mean vectors are provided with minimum volume properties. The univariate case with unknown variances is included.

Suggested Citation

  • Bedbur, S. & Lennartz, J.M. & Kamps, U., 2020. "On minimum volume properties of some confidence regions for multiple multivariate normal means," Statistics & Probability Letters, Elsevier, vol. 158(C).
    • Handle: RePEc:eee:stapro:v:158:y:2020:i:c:s0167715219303220
    DOI: 10.1016/j.spl.2019.108676
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    References listed on IDEAS

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    1. Bradley Efron, 2006. "Minimum volume confidence regions for a multivariate normal mean vector," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(4), pages 655-670, September.
    2. Jeyaratnam, S., 1985. "Minimum volume confidence regions," Statistics & Probability Letters, Elsevier, vol. 3(6), pages 307-308, October.
    3. Richard Samworth, 2005. "Small confidence sets for the mean of a spherically symmetric distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(3), pages 343-361, June.
    4. Kotz,Samuel & Nadarajah,Saralees, 2004. "Multivariate T-Distributions and Their Applications," Cambridge Books, Cambridge University Press, number 9780521826549.
    5. Nobuo Shinozaki, 1989. "Improved confidence sets for the mean of a multivariate normal distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(2), pages 331-346, June.
    Full references (including those not matched with items on IDEAS)

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