- Türkiye İstatistik Derneği Dergisi
- Vol: 7 Issue: 1
- A Note On Confidence Regions Based On The Bivariate Chebyshev Inequality. Applications To Order Stat...
A Note On Confidence Regions Based On The Bivariate Chebyshev Inequality. Applications To Order Statistics And Data
Authors : Jorge Navarro
Pages : 1-14
View : 9 | Download : 4
Publication Date : 2014-01-31
Article Type : Research
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