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Fiducial inference on the largest mean of a multivariate normal distribution

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  • Wandler, Damian V.
  • Hannig, Jan

Abstract

Inference on the largest mean of a multivariate normal distribution is a surprisingly difficult and unexplored topic. Difficulties arise when two or more of the means are simultaneously the largest mean. Our proposed solution is based on an extension of R.A. Fisher's fiducial inference methods termed generalized fiducial inference. We use a model selection technique along with the generalized fiducial distribution to allow for equal largest means and alleviate the overestimation that commonly occurs. Our proposed confidence intervals for the largest mean have asymptotically correct frequentist coverage and simulation results suggest that they possess promising small sample empirical properties. In addition to the theoretical calculations and simulations we also applied this approach to the air quality index of the four largest cities in the northeastern United States (Baltimore, Boston, New York, and Philadelphia).

Suggested Citation

  • Wandler, Damian V. & Hannig, Jan, 2011. "Fiducial inference on the largest mean of a multivariate normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 87-104, January.
    • Handle: RePEc:eee:jmvana:v:102:y:2011:i:1:p:87-104
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    References listed on IDEAS

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    1. Hannig, Jan & Iyer, Hari & Patterson, Paul, 2006. "Fiducial Generalized Confidence Intervals," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 254-269, March.
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    1. Hannig, Jan & Lai, Randy C.S. & Lee, Thomas C.M., 2014. "Computational issues of generalized fiducial inference," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 849-858.
    2. Liang Yan & Rui Wang & Xingzhong Xu, 2017. "Fiducial inference in the classical errors-in-variables model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(1), pages 93-114, January.

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