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

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 (X;Y ). The regions depend on the means, the variances and the (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 (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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