A Note On Confidence Regions Based On The Bivariate Chebyshev Inequality. Applications To Order Statistics And Data
A Note On Confidence Regions Based On The Bivariate Chebyshev Inequality. Applications To Order Statistics And Data
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
Keywords:
Chebyshev (Tchebychev) inequality, Mahalanobis distance, Principal components, Ellipsoid, Order statistics Bivariate box plots,
___
- Arnold, B.C., Balakrishnan, N. and Nagaraja, H.N.(2008). A First Course in Order Statistics. Classic ed., SIAM, Philadelphia, Pennsylvania.
- Budny, K. (2014). A generalization of Chebyshev’s inequality for Hilbert-space-valued random elements. Statistics & Probability Letters, 88, 62-65.
- Chen, X. (2011). A new generalization of Chebyshev inequality for random vectors. ArXiv:0707.0805v2.
- Fisher, R.A. (1936). The use of multiple measurements in taxonomic problems. Annals of Eugenics, 7, Part II, 179-188.
- Marshall, A.W. and Olkin, I. (1960). Multivariate Chebyshev inequalities. The Annals of Mathematical Statistics, 31, 1001-1014.
- Navarro, J. (2014). A very simple proof of the multivariate Chebyshev’s inequality. DOI:10.1080/03610926.2013.873135.
- Navarro, J. (2014). Can the bounds in the multivariate Chebyshev inequality be attained?. Statistics & Probability Letters, 91, 1-5.
- Navarro, J. and Balakrishnan, N. (2010). Study of some measures of dependence between order statistics and systems. Journal of Multivariate Analysis, 101, 52-67.
- Prakasa Rao, B.L.S. (2010). Chebyshev’s inequality for Hilbert-space-valued random elements. Statistics & Probability Letters, 80, 1039-1042.
- Zhou, L. and Hu, Z.C. (2012). Chebyshev’s inequality for Banach-space-valued random elements. Statistics & Probability Letters, 82, 925-931.
- ISSN: 1300-4077
- Başlangıç: 1998
- Yayıncı: Başbakanlık