On the exact distribution of linear combinations of order statistics from dependent random variables

Reinaldo B. Arellano-Valle; Marc G. Genton

doi:10.1016/j.jmva.2006.12.003

On the exact distribution of linear combinations of order statistics from dependent random variables

Reinaldo B. Arellano-Valle, Marc G. Genton^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

45 Scopus citations

Abstract

We study the exact distribution of linear combinations of order statistics of arbitrary (absolutely continuous) dependent random variables. In particular, we examine the case where the random variables have a joint elliptically contoured distribution and the case where the random variables are exchangeable. We investigate also the particular L-statistics that simply yield a set of order statistics, and study their joint distribution. We present the application of our results to genetic selection problems, design of cellular phone receivers, and visual acuity. We give illustrative examples based on the multivariate normal and multivariate Student t distributions.

Original language	English (US)
Pages (from-to)	1876-1894
Number of pages	19
Journal	JOURNAL OF MULTIVARIATE ANALYSIS
Volume	98
Issue number	10
DOIs	https://doi.org/10.1016/j.jmva.2006.12.003
State	Published - Nov 2007
Externally published	Yes

Keywords

Elliptically contoured
Exchangeable
Fundamental skew distribution
Kurtosis
Maximum
Selection mechanism
Skewness

ASJC Scopus subject areas

Statistics and Probability
Numerical Analysis
Statistics, Probability and Uncertainty

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10.1016/j.jmva.2006.12.003

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title = "On the exact distribution of linear combinations of order statistics from dependent random variables",

abstract = "We study the exact distribution of linear combinations of order statistics of arbitrary (absolutely continuous) dependent random variables. In particular, we examine the case where the random variables have a joint elliptically contoured distribution and the case where the random variables are exchangeable. We investigate also the particular L-statistics that simply yield a set of order statistics, and study their joint distribution. We present the application of our results to genetic selection problems, design of cellular phone receivers, and visual acuity. We give illustrative examples based on the multivariate normal and multivariate Student t distributions.",

keywords = "Elliptically contoured, Exchangeable, Fundamental skew distribution, Kurtosis, Maximum, Selection mechanism, Skewness",

author = "Arellano-Valle, {Reinaldo B.} and Genton, {Marc G.}",

note = "Funding Information: The authors thank two anonymous referees for suggestions that improved the paper. This research was partially supported by Grant FONDECYT 1040865/7050091-Chile and by NSF Grant DMS-0504896.",

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AU - Arellano-Valle, Reinaldo B.

AU - Genton, Marc G.

N1 - Funding Information: The authors thank two anonymous referees for suggestions that improved the paper. This research was partially supported by Grant FONDECYT 1040865/7050091-Chile and by NSF Grant DMS-0504896.

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Y1 - 2007/11

N2 - We study the exact distribution of linear combinations of order statistics of arbitrary (absolutely continuous) dependent random variables. In particular, we examine the case where the random variables have a joint elliptically contoured distribution and the case where the random variables are exchangeable. We investigate also the particular L-statistics that simply yield a set of order statistics, and study their joint distribution. We present the application of our results to genetic selection problems, design of cellular phone receivers, and visual acuity. We give illustrative examples based on the multivariate normal and multivariate Student t distributions.

AB - We study the exact distribution of linear combinations of order statistics of arbitrary (absolutely continuous) dependent random variables. In particular, we examine the case where the random variables have a joint elliptically contoured distribution and the case where the random variables are exchangeable. We investigate also the particular L-statistics that simply yield a set of order statistics, and study their joint distribution. We present the application of our results to genetic selection problems, design of cellular phone receivers, and visual acuity. We give illustrative examples based on the multivariate normal and multivariate Student t distributions.

KW - Elliptically contoured

KW - Exchangeable

KW - Fundamental skew distribution

KW - Kurtosis

KW - Maximum

KW - Selection mechanism

KW - Skewness

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On the exact distribution of linear combinations of order statistics from dependent random variables

Abstract

Keywords

ASJC Scopus subject areas

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