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A note on C. G. Khatri's and a Scott's papers on multivariate normal distributions

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Summary

The method used by C. G. Khatri [4] and by A. Scott [5] for proving certain inequalities for multivariate normal distributions seems to be attractive and powerful. However, we shall show here that this method is incorrect.

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References

  1. Halperin, M. (1967). An inequality on a bivariate Student's “t” distribution.J. Amer. Statist. Assoc.,62, 603–606.

    Article  MathSciNet  Google Scholar 

  2. Jogdeo, K. (1970). A simple proof of an inequality for multivariate normal probabilities of rectangles.Ann. Math. Statist.,41, 1357–1359.

    MathSciNet  Google Scholar 

  3. Khatri, C. G. (1967). On certain inequalities for normal distributions and their applications to simultaneous confidence bounds.Ann. Math. Statist.,38, 1853–1867.

    MathSciNet  Google Scholar 

  4. Khatri, C. G. (1970). Further contributions to some inequalities for normal distributions and their applications to simultaneous confidence bounds.Ann. Inst. Statist. Math.,22, 451–458.

    Article  MathSciNet  Google Scholar 

  5. Scott, A. (1967). A note on conservative confidence regions for the mean of a multivariate normal.Ann. Math. Statist.,38, 278–280. Correction:Ann. Math. Statist.,39 (1968), 2161.

    MathSciNet  Google Scholar 

  6. Šidák, Z. (1967). Rectangular confidence regions for the means of multivariate normal distributions,J. Amer. Statist. Assoc.,62, 626–633.

    Article  MathSciNet  Google Scholar 

  7. Šidák, Z. (1967). Rectangular confidence regions for the means of multivariate normal distributions, II,Statist. Lab. Publ., No. 7, Michigan State Univ.

  8. Šidák, Z. (1968). On multivariate normal probabilities of rectangles: their dependence on correlations.Ann. Math. Statist.,39, 1425–1434.

    MathSciNet  Google Scholar 

  9. Šidák, Z. (1971). On probabilities of rectangles in multivariate Student distributions: their dependence on correlations,Ann. Math. Statist.,42, 169–175.

    MathSciNet  Google Scholar 

  10. Tong, Y. L. (1970). Some probability inequalities of multivariate normal and multivariatet, J. Amer. Statist. Assoc.,65, 1243–1247.

    Article  Google Scholar 

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Authors and Affiliations

  1. Mathematical institute, Czechoslovak Academy of Sciences, Czechslovakia

    Zbyněk Šidák

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  1. Zbyněk Šidák
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Šidák, Z. A note on C. G. Khatri's and a Scott's papers on multivariate normal distributions. Ann Inst Stat Math 27, 181–184 (1975). https://doi.org/10.1007/BF02504636

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  • DOI: https://doi.org/10.1007/BF02504636

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