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On the confidence region for the bivariate co-ordinate-wise quantiles of the continuous bivariate distribution functions


  • Barakat, H. M.


In this paper, the distribution-free confidence region (rectangular) for the vector of the co-ordinate-wise quantiles of a general continuous bivariate distribution function is explicitly derived. This confidence region, in general, depends on the dependence function. A procedure is suggested which enables one to attach a confidence coefficient to the estimate of the confidence region even if the dependence function is unknown. Moreover, some approximated distribution-free lower bounds, which are independent of the dependence function, of the confidence coefficient of this region are derived. Finally, some results of this study are extended to the three-dimensional vector of the co-ordinate-wise quantiles.

Suggested Citation

  • Barakat, H. M., 2002. "On the confidence region for the bivariate co-ordinate-wise quantiles of the continuous bivariate distribution functions," Statistics & Probability Letters, Elsevier, vol. 56(1), pages 37-43, January.
  • Handle: RePEc:eee:stapro:v:56:y:2002:i:1:p:37-43

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    References listed on IDEAS

    1. Barry Arnold & Robert Beaver & Richard Groeneveld & William Meeker, 1993. "The nontruncated marginal of a truncated bivariate normal distribution," Psychometrika, Springer;The Psychometric Society, vol. 58(3), pages 471-488, September.
    2. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
    3. Jiang, Jiming, 1997. "Sharp upper and lower bounds for asymptotic levels of some statistical tests," Statistics & Probability Letters, Elsevier, vol. 35(4), pages 395-400, November.
    4. Aigner, Dennis & Lovell, C. A. Knox & Schmidt, Peter, 1977. "Formulation and estimation of stochastic frontier production function models," Journal of Econometrics, Elsevier, vol. 6(1), pages 21-37, July.
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