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A central limit theorem for a sequence of conditionally centered random fields

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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A central limit theorem for a sequence of conditionally centered random fields. / Jalilian, Abdollah; Poinas, Arnaud; Xu, Ganggang et al.
In: Bernoulli, Vol. 31, No. 4, 01.11.2025, p. 2675-2698.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Jalilian, A, Poinas, A, Xu, G & Waagepetersen, R 2025, 'A central limit theorem for a sequence of conditionally centered random fields', Bernoulli, vol. 31, no. 4, pp. 2675-2698. https://doi.org/10.3150/24-bej1821

APA

Jalilian, A., Poinas, A., Xu, G., & Waagepetersen, R. (2025). A central limit theorem for a sequence of conditionally centered random fields. Bernoulli, 31(4), 2675-2698. Advance online publication. https://doi.org/10.3150/24-bej1821

Vancouver

Jalilian A, Poinas A, Xu G, Waagepetersen R. A central limit theorem for a sequence of conditionally centered random fields. Bernoulli. 2025 Nov 1;31(4):2675-2698. Epub 2025 Jul 11. doi: 10.3150/24-bej1821

Author

Jalilian, Abdollah ; Poinas, Arnaud ; Xu, Ganggang et al. / A central limit theorem for a sequence of conditionally centered random fields. In: Bernoulli. 2025 ; Vol. 31, No. 4. pp. 2675-2698.

Bibtex

@article{0c46ed14702b49ccb6a715cbedfae8e1,
title = "A central limit theorem for a sequence of conditionally centered random fields",
abstract = "A central limit theorem is established for a sum of random variables belonging to a sequence of random fields. The fields are assumed to have zero mean conditional on the past history and to satisfy certain conditional α-mixing conditions in space or time. Exploiting conditional centering and the space-time structure, the limiting normal distribution is obtained for increasing spatial domain, increasing length of the sequence, or both of these. The theorem is very well suited for establishing asymptotic normality in the context of unbiased estimating function inference for a wide range of space-time processes. This is pertinent given the abundance of space-time data. Two examples demonstrate the applicability of the theorem.",
author = "Abdollah Jalilian and Arnaud Poinas and Ganggang Xu and Rasmus Waagepetersen",
year = "2025",
month = jul,
day = "11",
doi = "10.3150/24-bej1821",
language = "English",
volume = "31",
pages = "2675--2698",
journal = "Bernoulli",
issn = "1350-7265",
publisher = "International Statistical Institute",
number = "4",

}

RIS

TY - JOUR

T1 - A central limit theorem for a sequence of conditionally centered random fields

AU - Jalilian, Abdollah

AU - Poinas, Arnaud

AU - Xu, Ganggang

AU - Waagepetersen, Rasmus

PY - 2025/7/11

Y1 - 2025/7/11

N2 - A central limit theorem is established for a sum of random variables belonging to a sequence of random fields. The fields are assumed to have zero mean conditional on the past history and to satisfy certain conditional α-mixing conditions in space or time. Exploiting conditional centering and the space-time structure, the limiting normal distribution is obtained for increasing spatial domain, increasing length of the sequence, or both of these. The theorem is very well suited for establishing asymptotic normality in the context of unbiased estimating function inference for a wide range of space-time processes. This is pertinent given the abundance of space-time data. Two examples demonstrate the applicability of the theorem.

AB - A central limit theorem is established for a sum of random variables belonging to a sequence of random fields. The fields are assumed to have zero mean conditional on the past history and to satisfy certain conditional α-mixing conditions in space or time. Exploiting conditional centering and the space-time structure, the limiting normal distribution is obtained for increasing spatial domain, increasing length of the sequence, or both of these. The theorem is very well suited for establishing asymptotic normality in the context of unbiased estimating function inference for a wide range of space-time processes. This is pertinent given the abundance of space-time data. Two examples demonstrate the applicability of the theorem.

U2 - 10.3150/24-bej1821

DO - 10.3150/24-bej1821

M3 - Journal article

VL - 31

SP - 2675

EP - 2698

JO - Bernoulli

JF - Bernoulli

SN - 1350-7265

IS - 4

ER -