Some results on covariance of function of order statistics

Yong cheng Qi

doi:10.1016/0167-7152(94)90141-4

Some results on covariance of function of order statistics

Yong cheng Qi

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Abstract

Let X_1:n ≤ X_2:n ≤ ⋯ ≤ X_n:n denote order statistics of n i.i.d. samples. It is proven that g(X_i:n) and g(X_{i + 1:n}) are nonnegatively correlated for any function g with finite variance. Some examples are also constructed to show that Ma's (1992b) conjecture, that g(X_i:n) and g(X_j;n) are nonnegatively correlated for any function g, is not true.

Original language	English (US)
Pages (from-to)	111-114
Number of pages	4
Journal	Statistics and Probability Letters
Volume	19
Issue number	2
DOIs	https://doi.org/10.1016/0167-7152(94)90141-4
State	Published - Jan 27 1994
Externally published	Yes

Keywords

Covariance
order statistics

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10.1016/0167-7152(94)90141-4

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title = "Some results on covariance of function of order statistics",

abstract = "Let X1:n ≤ X2:n ≤ ⋯ ≤ Xn:n denote order statistics of n i.i.d. samples. It is proven that g(Xi:n) and g(Xi + 1:n) are nonnegatively correlated for any function g with finite variance. Some examples are also constructed to show that Ma's (1992b) conjecture, that g(Xi:n) and g(Xj;n) are nonnegatively correlated for any function g, is not true.",

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author = "Qi, {Yong cheng}",

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N2 - Let X1:n ≤ X2:n ≤ ⋯ ≤ Xn:n denote order statistics of n i.i.d. samples. It is proven that g(Xi:n) and g(Xi + 1:n) are nonnegatively correlated for any function g with finite variance. Some examples are also constructed to show that Ma's (1992b) conjecture, that g(Xi:n) and g(Xj;n) are nonnegatively correlated for any function g, is not true.

AB - Let X1:n ≤ X2:n ≤ ⋯ ≤ Xn:n denote order statistics of n i.i.d. samples. It is proven that g(Xi:n) and g(Xi + 1:n) are nonnegatively correlated for any function g with finite variance. Some examples are also constructed to show that Ma's (1992b) conjecture, that g(Xi:n) and g(Xj;n) are nonnegatively correlated for any function g, is not true.

KW - Covariance

KW - order statistics

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JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 2

ER -

Some results on covariance of function of order statistics

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Keywords

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