Point process convergence for the off-diagonal entries of sample covariance matrices

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Point process convergence for the off-diagonal entries of sample covariance matrices. / Heiny, Johannes; Mikosch, Thomas; Yslas, Jorge.

In: Annals of Applied Probability, Vol. 31, No. 2, 2021, p. 538-560.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Heiny, J, Mikosch, T & Yslas, J 2021, 'Point process convergence for the off-diagonal entries of sample covariance matrices', Annals of Applied Probability, vol. 31, no. 2, pp. 538-560. https://doi.org/10.1214/20-AAP1597

APA

Heiny, J., Mikosch, T., & Yslas, J. (2021). Point process convergence for the off-diagonal entries of sample covariance matrices. Annals of Applied Probability, 31(2), 538-560. https://doi.org/10.1214/20-AAP1597

Vancouver

Heiny J, Mikosch T, Yslas J. Point process convergence for the off-diagonal entries of sample covariance matrices. Annals of Applied Probability. 2021;31(2):538-560. https://doi.org/10.1214/20-AAP1597

Author

Heiny, Johannes ; Mikosch, Thomas ; Yslas, Jorge. / Point process convergence for the off-diagonal entries of sample covariance matrices. In: Annals of Applied Probability. 2021 ; Vol. 31, No. 2. pp. 538-560.

Bibtex

@article{24b73710b2e243a1926232c769bb2bed,
title = "Point process convergence for the off-diagonal entries of sample covariance matrices",
abstract = "We study point process convergence for sequences of i.i.d. random walks. The objective is to derive asymptotic theory for the extremes of these random walks. We show convergence of the maximum random walk to the Gumbel distribution under the existence of a (2+δ)th moment. We make heavy use of precise large deviation results for sums of i.i.d. random variables. As a consequence, we derive the joint convergence of the off-diagonal entries in sample covariance and correlation matrices of a high-dimensional sample whose dimension increases with the sample size. This generalizes known results on the asymptotic Gumbel property of the largest entry.",
author = "Johannes Heiny and Thomas Mikosch and Jorge Yslas",
year = "2021",
doi = "10.1214/20-AAP1597",
language = "English",
volume = "31",
pages = "538--560",
journal = "Annals of Applied Probability",
issn = "1050-5164",
publisher = "Institute of Mathematical Statistics",
number = "2",

}

RIS

TY - JOUR

T1 - Point process convergence for the off-diagonal entries of sample covariance matrices

AU - Heiny, Johannes

AU - Mikosch, Thomas

AU - Yslas, Jorge

PY - 2021

Y1 - 2021

N2 - We study point process convergence for sequences of i.i.d. random walks. The objective is to derive asymptotic theory for the extremes of these random walks. We show convergence of the maximum random walk to the Gumbel distribution under the existence of a (2+δ)th moment. We make heavy use of precise large deviation results for sums of i.i.d. random variables. As a consequence, we derive the joint convergence of the off-diagonal entries in sample covariance and correlation matrices of a high-dimensional sample whose dimension increases with the sample size. This generalizes known results on the asymptotic Gumbel property of the largest entry.

AB - We study point process convergence for sequences of i.i.d. random walks. The objective is to derive asymptotic theory for the extremes of these random walks. We show convergence of the maximum random walk to the Gumbel distribution under the existence of a (2+δ)th moment. We make heavy use of precise large deviation results for sums of i.i.d. random variables. As a consequence, we derive the joint convergence of the off-diagonal entries in sample covariance and correlation matrices of a high-dimensional sample whose dimension increases with the sample size. This generalizes known results on the asymptotic Gumbel property of the largest entry.

U2 - 10.1214/20-AAP1597

DO - 10.1214/20-AAP1597

M3 - Journal article

VL - 31

SP - 538

EP - 560

JO - Annals of Applied Probability

JF - Annals of Applied Probability

SN - 1050-5164

IS - 2

ER -

ID: 302075064