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Inadmissibility of the best equivariant predictive density in the unknown variance case

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  • A. Boisbunon
  • Y. Maruyama

Abstract

This work treats the problem of estimating the predictive density of a random vector when both the mean vector and the variance are unknown. We prove that the density of reference in this context is inadmissible under the Kullback–Leibler loss in a nonasymptotic framework. Our result holds even when the dimension of the vector is strictly lower than three, which is surprising compared to the known variance setting. Finally, we discuss the relationship between the prediction and the estimation problems.

Suggested Citation

  • A. Boisbunon & Y. Maruyama, 2014. "Inadmissibility of the best equivariant predictive density in the unknown variance case," Biometrika, Biometrika Trust, vol. 101(3), pages 733-740.
    • Handle: RePEc:oup:biomet:v:101:y:2014:i:3:p:733-740.
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    File URL: http://hdl.handle.net/10.1093/biomet/asu024
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    Cited by:

    1. Malay Ghosh & Tatsuya Kubokawa & Gauri Sankar Datta, 2020. "Density Prediction and the Stein Phenomenon," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(2), pages 330-352, August.
    2. Fourdrinier, Dominique & Marchand, Éric & Strawderman, William E., 2019. "On efficient prediction and predictive density estimation for normal and spherically symmetric models," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 18-25.

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