A remark on quadrant normal probabilities in high dimensions

Yosef Rinott; Vladimir Rotar

doi:10.1016/S0167-7152(00)00141-3

A remark on quadrant normal probabilities in high dimensions

Yosef Rinott
, Vladimir Rotar^*

^*Corresponding author for this work

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

10 Scopus citations

Abstract

This paper provides an asymptotic evaluation of the quadrant probability P(Y₁≤b,…, Y_t≤b) as t→∞, where the Y_i's are exchangeable normals with a correlation ρ. This probability is often represented as ∫-∞∞Φ^t(x)dΦ(a^1/2(x-b)), where Φ is the standard normal distribution, and a=(1-ρ)/ρ.

Original language	English
Pages (from-to)	47-51
Number of pages	5
Journal	Statistics and Probability Letters
Volume	51
Issue number	1
DOIs	https://doi.org/10.1016/S0167-7152(00)00141-3
State	Published - 1 Jan 2001
Externally published	Yes

Keywords

Correlations
Laplace method
Maximum of dependent normal variables
Normal probabilities
Primary 62E20
Secondary 60E05

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10.1016/S0167-7152(00)00141-3

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AB - This paper provides an asymptotic evaluation of the quadrant probability P(Y1≤b,…, Yt≤b) as t→∞, where the Yi's are exchangeable normals with a correlation ρ. This probability is often represented as ∫-∞∞Φt(x)dΦ(a1/2(x-b)), where Φ is the standard normal distribution, and a=(1-ρ)/ρ.

KW - Correlations

KW - Laplace method

KW - Maximum of dependent normal variables

KW - Normal probabilities

KW - Primary 62E20

KW - Secondary 60E05

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A remark on quadrant normal probabilities in high dimensions

Abstract

Keywords

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