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Weak convergence of partial sums of absolutely regular sequences

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  • Eberlein, Ernst

Abstract

We show that weak convergence results for partial sums of absolutely regular sequences can easily be derived from the corresponding convergence results for independent triangular arrays. The link to be used is a simple lemma on the total variation norm.

Suggested Citation

  • Eberlein, Ernst, 1984. "Weak convergence of partial sums of absolutely regular sequences," Statistics & Probability Letters, Elsevier, vol. 2(5), pages 291-293, October.
    • Handle: RePEc:eee:stapro:v:2:y:1984:i:5:p:291-293
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    Citations

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    Cited by:

    1. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2013. "Testing Many Moment Inequalities," CeMMAP working papers 65/13, Institute for Fiscal Studies.
    2. Moosup Kim & Sangyeol Lee, 2019. "Test for tail index constancy of GARCH innovations based on conditional volatility," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(4), pages 947-981, August.
    3. Victor Chernozhukov & Denis Chetverikov & Kengo Kato & Aureo de Paula, 2019. "Inference on Causal and Structural Parameters using Many Moment Inequalities," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(5), pages 1867-1900.
    4. Drees, Holger & Janßen, Anja & Neblung, Sebastian, 2021. "Cluster based inference for extremes of time series," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 1-33.
    5. Arcones, Miguel A., 1995. "On the central limit theorem for U-statistics under absolute regularity," Statistics & Probability Letters, Elsevier, vol. 24(3), pages 245-249, August.
    6. Rootzén, Holger, 2009. "Weak convergence of the tail empirical process for dependent sequences," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 468-490, February.
    7. Xiaohong Chen & Yuan Liao & Weichen Wang, 2022. "Inference on Time Series Nonparametric Conditional Moment Restrictions Using General Sieves," Papers 2301.00092, arXiv.org, revised Jan 2023.
    8. Salim Bouzebda & Boutheina Nemouchi, 2023. "Weak-convergence of empirical conditional processes and conditional U-processes involving functional mixing data," Statistical Inference for Stochastic Processes, Springer, vol. 26(1), pages 33-88, April.

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