IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v47y2000i2p115-124.html
   My bibliography  Save this article

A more general central limit theorem for m-dependent random variables with unbounded m

Author

Listed:
  • Romano, Joseph P.
  • Wolf, Michael

Abstract

In this article, a general central limit theorem for a triangular array of m-dependent random variables is presented. Here, m may tend to infinity with the row index at a certain rate. Our theorem is a generalization of previous results. Some examples are given that show that the generalization is useful. In particular, we consider the limiting behavior of the sample mean of a combined sample of independent long-memory sequences, the limiting behavior of a spectral estimator, and the moving blocks bootstrap distribution. The examples make it clear the consideration of asymptotic behavior with the amount of dependence m increasing with n is useful even when the underlying processes are weakly dependent (or even independent), because certain natural statistics that arise in the analysis of time series have this structure. In addition, we provide an example to demonstrate the sharpness of our result.

Suggested Citation

  • Romano, Joseph P. & Wolf, Michael, 2000. "A more general central limit theorem for m-dependent random variables with unbounded m," Statistics & Probability Letters, Elsevier, vol. 47(2), pages 115-124, April.
    • Handle: RePEc:eee:stapro:v:47:y:2000:i:2:p:115-124
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(99)00146-7
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

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

    Citations

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


    Cited by:

    1. Jing Dong & Rouba Ibrahimb, 2020. "Managing Supply in the On-Demand Economy: Flexible Workers, Full-Time Employees, or Both?," Operations Research, INFORMS, vol. 68(4), pages 1238-1264, July.
    2. Le Breton, Michel & Lepelley, Dominique & Smaoui, Hatem, 2012. "The Probability of Casting a Decisive Vote: From IC to IAC trhough Ehrhart's Polynomials and Strong Mixing," IDEI Working Papers 722, Institut d'Économie Industrielle (IDEI), Toulouse.
    3. Aristide Houndetoungan & Abdoul Haki Maoude, 2024. "Inference for Two-Stage Extremum Estimators," Papers 2402.05030, arXiv.org.
    4. Bücher, Axel & Kojadinovic, Ivan & Rohmer, Tom & Segers, Johan, 2014. "Detecting changes in cross-sectional dependence in multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 111-128.
    5. James G. MacKinnon & Matthew D. Webb & Morten Ø. Nielsen, 2017. "Bootstrap And Asymptotic Inference With Multiway Clustering," Working Paper 1386, Economics Department, Queen's University.
    6. Jacek Leśkow & Rafał Synowiecki, 2010. "On bootstrapping periodic random arrays with increasing period," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 71(3), pages 253-279, May.
    7. Ayyala, Deepak Nag & Park, Junyong & Roy, Anindya, 2017. "Mean vector testing for high-dimensional dependent observations," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 136-155.
    8. Last, Michael & Shumway, Robert, 2008. "Detecting abrupt changes in a piecewise locally stationary time series," Journal of Multivariate Analysis, Elsevier, vol. 99(2), pages 191-214, February.
    9. Chan, Terence, 2022. "On a new class of continuous indices of inequality," Mathematical Social Sciences, Elsevier, vol. 120(C), pages 8-23.
    10. Kojadinovic, Ivan & Rohmer, Tom & Segers, Johan, 2013. "Detecting changes in cross-sectional dependence in multivariate time series," LIDAM Discussion Papers ISBA 2013051, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    11. Jiti Gao & Guangming Pan & Yanrong Yang & Bo Zhang, 2019. "Estimation of Cross-Sectional Dependence in Large Panels," Papers 1904.06843, arXiv.org.
    12. Aristide Houndetoungan & Abdoul Haki Maoude, 2024. "Inference for Two-Stage Extremum Estimators," THEMA Working Papers 2024-01, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    13. Harvey, Danielle J. & Weng, Qian & Beckett, Laurel A., 2010. "On an asymptotic distribution of dependent random variables on a 3-dimensional lattice," Statistics & Probability Letters, Elsevier, vol. 80(11-12), pages 1015-1021, June.
    14. Zhao, Zhibiao, 2010. "Density estimation for nonlinear parametric models with conditional heteroscedasticity," Journal of Econometrics, Elsevier, vol. 155(1), pages 71-82, March.
    15. Giuseppe Cavaliere & Dimitris N. Politis & Anders Rahbek & Marco Meyer & Jens-Peter Kreiss, 2015. "Recent developments in bootstrap methods for dependent data," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(3), pages 377-397, May.
    16. Zhao, Zhibiao & Wu, Wei Biao, 2007. "Asymptotic theory for curve-crossing analysis," Stochastic Processes and their Applications, Elsevier, vol. 117(7), pages 862-877, July.
    17. Atsushi Inoue, 2015. "Comment," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(1), pages 9-11, January.
    18. Jiti Gao & Guangming Pan & Yanrong Yang, 2016. "CEstimation of Structural Breaks in Large Panels with Cross-Sectional Dependence," Monash Econometrics and Business Statistics Working Papers 12/16, Monash University, Department of Econometrics and Business Statistics.
    19. Geenens, Gery & Simar, Léopold, 2010. "Nonparametric tests for conditional independence in two-way contingency tables," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 765-788, April.
    20. Hui, Francis K.C. & Geenens, Gery, 2012. "Nonparametric bootstrap tests of conditional independence in two-way contingency tables," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 130-144.
    21. Jiti Gao & Guangming Pan & Yanrong Yang & Bo Zhang, 2019. "An Integrated Panel Data Approach to Modelling Economic Growth," Monash Econometrics and Business Statistics Working Papers 9/19, Monash University, Department of Econometrics and Business Statistics.

    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:stapro:v:47:y:2000:i:2:p:115-124. 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.

    We have no bibliographic references for this item. You can help adding them by using 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/622892/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.