A Note On Confidence Regions Based On The Bivariate Chebyshev Inequality. Applications To Order Statistics And Data

Authors : Jorge NAVARRO

Pages : 1-14

View : 38 | Download : 8

Publication Date : 2014-01-31

Article Type : Research Paper

Abstract :Chebyshev’s inequality was recently extended to the multivariate case. In this paper this new  inequality is used to obtain distribution-free confidence regions for an arbitrary bivariate random vector  insert ignore into journalissuearticles values(X;Y );. The regions depend on the means, the variances and the insert ignore into journalissuearticles values(Pearson); correlation coefficient. The theoretical method is illustrated by computing the confidence regions for two order statistics obtained from  a sample of iid random variables or obtained from a sequence of dependent components. They are also  computed for an arbitrary bivariate data set insert ignore into journalissuearticles values(with or without groups); by obtaining plots similar to univariate  box plots.
Keywords : Chebyshev Tchebychev, inequality, Mahalanobis distance, Principal components, Ellipsoid, Order statistics, Bivariate box plots

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