IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v124y2014i12p4012-4029.html
   My bibliography  Save this article

An invariance principle for stationary random fields under Hannan’s condition

Author

Listed:
  • Volný, Dalibor
  • Wang, Yizao

Abstract

We establish an invariance principle for a general class of stationary random fields indexed by Zd, under Hannan’s condition generalized to Zd. To do so we first establish a uniform integrability result for stationary orthomartingales, and second we establish a coboundary decomposition for certain stationary random fields. At last, we obtain an invariance principle by developing an orthomartingale approximation. Our invariance principle improves known results in the literature, and particularly we require only finite second moment.

Suggested Citation

  • Volný, Dalibor & Wang, Yizao, 2014. "An invariance principle for stationary random fields under Hannan’s condition," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 4012-4029.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:12:p:4012-4029
    DOI: 10.1016/j.spa.2014.07.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414914001744
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2014.07.015?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. El Machkouri, Mohamed & Volný, Dalibor & Wu, Wei Biao, 2013. "A central limit theorem for stationary random fields," Stochastic Processes and their Applications, Elsevier, vol. 123(1), pages 1-14.
    2. Volný, Dalibor, 1993. "Approximating martingales and the central limit theorem for strictly stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 44(1), pages 41-74, January.
    3. Poghosyan, S. & Roelly, S., 1998. "Invariance principle for martingale-difference random fields," Statistics & Probability Letters, Elsevier, vol. 38(3), pages 235-245, June.
    4. Bradley, Richard C., 1989. "A caution on mixing conditions for random fields," Statistics & Probability Letters, Elsevier, vol. 8(5), pages 489-491, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Peligrad, Magda & Zhang, Na, 2018. "On the normal approximation for random fields via martingale methods," Stochastic Processes and their Applications, Elsevier, vol. 128(4), pages 1333-1346.
    2. Magda Peligrad & Dalibor Volný, 2020. "Quenched Invariance Principles for Orthomartingale-Like Sequences," Journal of Theoretical Probability, Springer, vol. 33(3), pages 1238-1265, September.
    3. Lin, Han-Mai & Merlevède, Florence, 2022. "On the weak invariance principle for ortho-martingale in Banach spaces. Application to stationary random fields," Stochastic Processes and their Applications, Elsevier, vol. 153(C), pages 198-220.
    4. Michael C. Tseng, 2019. "A 2-Dimensional Functional Central Limit Theorem for Non-stationary Dependent Random Fields," Papers 1910.02577, arXiv.org.
    5. Klicnarová, Jana & Volný, Dalibor & Wang, Yizao, 2016. "Limit theorems for weighted Bernoulli random fields under Hannan’s condition," Stochastic Processes and their Applications, Elsevier, vol. 126(6), pages 1819-1838.
    6. Guy Cohen & Jean-Pierre Conze, 2017. "CLT for Random Walks of Commuting Endomorphisms on Compact Abelian Groups," Journal of Theoretical Probability, Springer, vol. 30(1), pages 143-195, March.
    7. Na Zhang & Lucas Reding & Magda Peligrad, 2020. "On the Quenched Central Limit Theorem for Stationary Random Fields Under Projective Criteria," Journal of Theoretical Probability, Springer, vol. 33(4), pages 2351-2379, December.
    8. Tempelman, Arkady, 2022. "Randomized multivariate Central Limit Theorems for ergodic homogeneous random fields," Stochastic Processes and their Applications, Elsevier, vol. 143(C), pages 89-105.
    9. Volný, Dalibor, 2019. "On limit theorems for fields of martingale differences," Stochastic Processes and their Applications, Elsevier, vol. 129(3), pages 841-859.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Klicnarová, Jana & Volný, Dalibor & Wang, Yizao, 2016. "Limit theorems for weighted Bernoulli random fields under Hannan’s condition," Stochastic Processes and their Applications, Elsevier, vol. 126(6), pages 1819-1838.
    2. Richard C. Bradley, 2001. "A Stationary Rho-Mixing Markov Chain Which Is Not “Interlaced” Rho-Mixing," Journal of Theoretical Probability, Springer, vol. 14(3), pages 717-727, July.
    3. Hagemann, Andreas, 2019. "Placebo inference on treatment effects when the number of clusters is small," Journal of Econometrics, Elsevier, vol. 213(1), pages 190-209.
    4. Peligrad, Magda & Zhang, Na, 2018. "On the normal approximation for random fields via martingale methods," Stochastic Processes and their Applications, Elsevier, vol. 128(4), pages 1333-1346.
    5. Daniel Nordman, 2008. "An empirical likelihood method for spatial regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 68(3), pages 351-363, November.
    6. Zhou, Xing-cai & Lin, Jin-guan, 2012. "A wavelet estimator in a nonparametric regression model with repeated measurements under martingale difference error’s structure," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1914-1922.
    7. Victor Chernozhukov & Wolfgang Härdle & Chen Huang & Weining Wang, 2018. "LASSO-driven inference in time and space," CeMMAP working papers CWP36/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. Dalibor Volný, 2010. "Martingale Approximation and Optimality of Some Conditions for the Central Limit Theorem," Journal of Theoretical Probability, Springer, vol. 23(3), pages 888-903, September.
    9. Chen, Likai & Wang, Weining & Wu, Wei Biao, 2019. "Inference of Break-Points in High-Dimensional Time Series," IRTG 1792 Discussion Papers 2019-013, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    10. S. Lahiri & Kanchan Mukherjee, 2004. "Asymptotic distributions of M-estimators in a spatial regression model under some fixed and stochastic spatial sampling designs," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(2), pages 225-250, June.
    11. 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.
    12. Koch, Erwan & Dombry, Clément & Robert, Christian Y., 2019. "A central limit theorem for functions of stationary max-stable random fields on Rd," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3406-3430.
    13. Lin, Han-Mai & Merlevède, Florence, 2022. "On the weak invariance principle for ortho-martingale in Banach spaces. Application to stationary random fields," Stochastic Processes and their Applications, Elsevier, vol. 153(C), pages 198-220.
    14. Oka, Tatsushi & Qu, Zhongjun, 2011. "Estimating structural changes in regression quantiles," Journal of Econometrics, Elsevier, vol. 162(2), pages 248-267, June.
    15. Zhang, Rongmao & Chan, Ngai Hang & Chi, Changxiong, 2023. "Nonparametric testing for the specification of spatial trend functions," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    16. Kim, Tae-Sung & Ko, Mi-Hwa & Choi, Yong-Kab, 2008. "The invariance principle for linear multi-parameter stochastic processes generated by associated fields," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3298-3303, December.
    17. Burton, Robert M. & Steif, Jeffrey E., 1995. "Quite weak Bernoulli with exponential rate and percolation for random fields," Stochastic Processes and their Applications, Elsevier, vol. 58(1), pages 35-55, July.
    18. Tempelman, Arkady, 2022. "Randomized multivariate Central Limit Theorems for ergodic homogeneous random fields," Stochastic Processes and their Applications, Elsevier, vol. 143(C), pages 89-105.
    19. Magda Peligrad & Hailin Sang, 2013. "Central Limit Theorem for Linear Processes with Infinite Variance," Journal of Theoretical Probability, Springer, vol. 26(1), pages 222-239, March.
    20. Wu, Wei Biao, 2009. "An asymptotic theory for sample covariances of Bernoulli shifts," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 453-467, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:124:y:2014:i:12:p:4012-4029. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.