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Scaling transition and edge effects for negatively dependent linear random fields on Z2

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  • Surgailis, Donatas

Abstract

We obtain a complete description of anisotropic scaling limits and the existence of scaling transition for a class of negatively dependent linear random fields X on Z2 with moving-average coefficients a(t,s) decaying as |t|−q1 and |s|−q2 in the horizontal and vertical directions, q1−1+q2−1<1 and satisfying ∑(t,s)∈Z2a(t,s)=0. The scaling limits are taken over rectangles whose sides increase as λ and λγ when λ→∞, for any γ>0. The scaling transition occurs at γ0X>0 if the scaling limits of X are different and do not depend on γ for γ>γ0X and γ<γ0X. We prove that the scaling transition in this model is closely related to the presence or absence of the edge effects. The paper extends the results in Pilipauskaitė and Surgailis (2017) on the scaling transition for a related class of random fields with long-range dependence.

Suggested Citation

  • Surgailis, Donatas, 2020. "Scaling transition and edge effects for negatively dependent linear random fields on Z2," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7518-7546.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:12:p:7518-7546
    DOI: 10.1016/j.spa.2020.08.005
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    References listed on IDEAS

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    1. Pilipauskaitė, Vytautė & Surgailis, Donatas, 2014. "Joint temporal and contemporaneous aggregation of random-coefficient AR(1) processes," Stochastic Processes and their Applications, Elsevier, vol. 124(2), pages 1011-1035.
    2. Frédéric Lavancier, 2007. "Invariance principles for non-isotropic long memory random fields," Statistical Inference for Stochastic Processes, Springer, vol. 10(3), pages 255-282, October.
    3. Hira Koul & Nao Mimoto & Donatas Surgailis, 2016. "A goodness-of-fit test for marginal distribution of linear random fields with long memory," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(2), pages 165-193, February.
    4. Puplinskaitė, Donata & Surgailis, Donatas, 2015. "Scaling transition for long-range dependent Gaussian random fields," Stochastic Processes and their Applications, Elsevier, vol. 125(6), pages 2256-2271.
    5. Pilipauskaitė, Vytautė & Surgailis, Donatas, 2015. "Joint aggregation of random-coefficient AR(1) processes with common innovations," Statistics & Probability Letters, Elsevier, vol. 101(C), pages 73-82.
    6. Pilipauskaitė, Vytautė & Surgailis, Donatas, 2017. "Scaling transition for nonlinear random fields with long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 127(8), pages 2751-2779.
    7. Damarackas, Julius & Paulauskas, Vygantas, 2017. "Spectral covariance and limit theorems for random fields with infinite variance," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 156-175.
    8. Guo, Hongwen & Lim, Chae Young & Meerschaert, Mark M., 2009. "Local Whittle estimator for anisotropic random fields," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 993-1028, May.
    9. Lahiri, S.N. & Robinson, Peter M., 2016. "Central limit theorems for long range dependent spatial linear processes," LSE Research Online Documents on Economics 65331, London School of Economics and Political Science, LSE Library.
    10. Rosa Espejo & Nikolai Leonenko & Andriy Olenko & María Ruiz-Medina, 2015. "On a class of minimum contrast estimators for Gegenbauer random fields," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 657-680, December.
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    1. Surgailis, Donatas, 2024. "Scaling limits of nonlinear functions of random grain model, with application to Burgers’ equation," Stochastic Processes and their Applications, Elsevier, vol. 174(C).

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