Institute of Mathematical Statistics Collections

Reverse Exchangeability and Extreme Order Statistics

Yindeng Jiang and Michael D. Perlman

Full-text: Open access

Abstract

For a bivariate random vector $(X,Y)$, symmetry conditions are presented that yield stochastic orderings among $|X|$, $|Y|$, $|\max(X,Y)|$, and $|\min(X,Y)|$. Partial extensions of these results for multivariate random vectors $(X_{1},\ldots ,X_{n})$ are also given.

Chapter information

Source
Galin Jones and Xiaotong Shen, eds., Advances in Modern Statistical Theory and Applications: A Festschrift in honor of Morris L. Eaton, (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2013) , 83-101

Dates
First available in Project Euclid: 23 September 2013

Permanent link to this document
https://projecteuclid.org/euclid.imsc/1379942049

Digital Object Identifier
doi:10.1214/12-IMSCOLL1005

Mathematical Reviews number (MathSciNet)
MR3586940

Zentralblatt MATH identifier
1320.62110

Keywords
bivariate distribution extreme order statistics multivariate distribution reverse exchangeability symmetry

Rights
Copyright © 2013, Institute of Mathematical Statistics

Citation

Jiang, Yindeng; Perlman, Michael D. Reverse Exchangeability and Extreme Order Statistics. Advances in Modern Statistical Theory and Applications: A Festschrift in honor of Morris L. Eaton, 83--101, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2013. doi:10.1214/12-IMSCOLL1005. https://projecteuclid.org/euclid.imsc/1379942049


Export citation

References

  • Casella, G. and Berger, R. L. (2002). Statistical Inference. Duxbury Pacific Grove, CA.
  • Eaton, M. L. (1982). A review of selected topics in multivariate probability inequalities. The Annals of Statistics 10 11–43.
  • Eaton, M. L. (1987). Lectures on Topics in Probability Inequalities. Centrum voor Wiskunde en Informatica.
  • Eaton, M. L. and Perlman, M. D. (1977). Reflection groups, generalized Schur functions, and the geometry of majorization. The Annals of Probability 5 829–860.
  • Jiang, Y. (2009). Factor Model Monte Carlo Methods for General Fund-of-Funds Portfolio Management PhD thesis, University of Washington.