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March, 1977 An Ordering Theorem for Conditionally Independent and Identically Distributed Random Variables
Y. L. Tong
Ann. Statist. 5(2): 274-277 (March, 1977). DOI: 10.1214/aos/1176343794

Abstract

Let $\mathbf{a}$ and $\mathbf{b}$ be $r$-dimensional real vectors. It is shown that if $\mathbf{a}$ majorizes $\mathbf{b}$, then $E(\Pi^r_{j = 1} X_j^a j) \geqq E(\Pi^r_{j = 1} X_j^b j)$ holds for nonnegative random variables $X_1, \cdots, X_r$ whose joint pdf is permutation symmetric. If in addition the components of $\mathbf{a, b}$ are nonnegative integers, then for every Borel-measurable set $A$, $\Pi^r_{j = 1} P\lbrack\cap^{a_j}_{i = 1} \{Z_i \in A\}\rbrack \geqq \Pi^r_{j = 1} P\lbrack\cap^{b_j}_{i = 1} \{Z_i \in A\}\rbrack$ holds for conditionally i.i.d. random variables $Z_i$. Applications are considered.

Citation

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Y. L. Tong. "An Ordering Theorem for Conditionally Independent and Identically Distributed Random Variables." Ann. Statist. 5 (2) 274 - 277, March, 1977. https://doi.org/10.1214/aos/1176343794

Information

Published: March, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0365.60019
MathSciNet: MR433663
Digital Object Identifier: 10.1214/aos/1176343794

Subjects:
Primary: 26A86
Secondary: 62H99

Rights: Copyright © 1977 Institute of Mathematical Statistics

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Vol.5 • No. 2 • March, 1977
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