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On the confidence region for the bivariate co-ordinate-wise quantiles of the continuous bivariate distribution functions
Faculty
Not Specified
Year:
2002
Type of Publication:
Article
Pages:
37-43
Authors:
BARAKAT, HM
DOI:
10.1016/S0167-7152(01)00145-6
Journal:
STATISTICS \& PROBABILITY LETTERS ELSEVIER SCIENCE BV
Volume:
56
Research Area:
Mathematics
ISSN
ISI:000173266600005
Keywords :
distribution-free confidence region, bivariate order statistics, bivariate quantiles
Abstract:
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. (C) 2002 Elsevier Science B.V. All rights reserved.
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