IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v34y2021i1d10.1007_s10959-019-00973-2.html
   My bibliography  Save this article

The Marcinkiewicz–Zygmund-Type Strong Law of Large Numbers with General Normalizing Sequences

Author

Listed:
  • Vu T. N. Anh

    (Hoa Lu University)

  • Nguyen T. T. Hien

    (Vinh University)

  • Le V. Thanh

    (Vinh University)

  • Vo T. H. Van

    (Vinh University)

Abstract

This paper establishes complete convergence for weighted sums and the Marcinkiewicz–Zygmund-type strong law of large numbers for sequences of negatively associated and identically distributed random variables $$\{X,X_n,n\ge 1\}$$ { X , X n , n ≥ 1 } with general normalizing constants under a moment condition that $$ER(X)

Suggested Citation

  • Vu T. N. Anh & Nguyen T. T. Hien & Le V. Thanh & Vo T. H. Van, 2021. "The Marcinkiewicz–Zygmund-Type Strong Law of Large Numbers with General Normalizing Sequences," Journal of Theoretical Probability, Springer, vol. 34(1), pages 331-348, March.
    • Handle: RePEc:spr:jotpro:v:34:y:2021:i:1:d:10.1007_s10959-019-00973-2
    DOI: 10.1007/s10959-019-00973-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-019-00973-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10959-019-00973-2?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. Bing-Yi Jing & Han-Ying Liang, 2008. "Strong Limit Theorems for Weighted Sums of Negatively Associated Random Variables," Journal of Theoretical Probability, Springer, vol. 21(4), pages 890-909, December.
    2. A. Gut, 2004. "An Extension of the Kolmogorov–Feller Weak Law of Large Numbers with an Application to the St. Petersburg Game," Journal of Theoretical Probability, Springer, vol. 17(3), pages 769-779, July.
    3. Florian Hechner & Bernard Heinkel, 2010. "The Marcinkiewicz–Zygmund LLN in Banach Spaces: A Generalized Martingale Approach," Journal of Theoretical Probability, Springer, vol. 23(2), pages 509-522, June.
    4. Aiting Shen & Ying Zhang & Andrei Volodin, 2014. "On the Strong Convergence and Complete Convergence for Pairwise NQD Random Variables," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, May.
    5. Soo Hak Sung, 2014. "Marcinkiewicz–Zygmund Type Strong Law of Large Numbers for Pairwise i.i.d. Random Variables," Journal of Theoretical Probability, Springer, vol. 27(1), pages 96-106, March.
    6. Martikainen, Alexander, 1995. "On the strong law of large numbers for sums of pairwise independent random variables," Statistics & Probability Letters, Elsevier, vol. 25(1), pages 21-26, October.
    7. Burton, Robert M. & Dabrowski, AndréRobert & Dehling, Herold, 1986. "An invariance principle for weakly associated random vectors," Stochastic Processes and their Applications, Elsevier, vol. 23(2), pages 301-306, December.
    8. Soo Sung, 2011. "On the strong convergence for weighted sums of random variables," Statistical Papers, Springer, vol. 52(2), pages 447-454, May.
    9. Csörgo, Sándor & Simons, Gordon, 1996. "A strong law of large numbers for trimmed sums, with applications to generalized St. Petersburg games," Statistics & Probability Letters, Elsevier, vol. 26(1), pages 65-73, January.
    10. David Heath & Sidney Resnick & Gennady Samorodnitsky, 1998. "Heavy Tails and Long Range Dependence in On/Off Processes and Associated Fluid Models," Mathematics of Operations Research, INFORMS, vol. 23(1), pages 145-165, February.
    11. Matula, Przemyslaw, 1992. "A note on the almost sure convergence of sums of negatively dependent random variables," Statistics & Probability Letters, Elsevier, vol. 15(3), pages 209-213, October.
    Full references (including those not matched with items on IDEAS)

    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. Huang, Wen-Tao & Xu, Bing, 2002. "Some maximal inequalities and complete convergences of negatively associated random sequences," Statistics & Probability Letters, Elsevier, vol. 57(2), pages 183-191, April.
    2. Aiting Shen & Yu Zhang & Benqiong Xiao & Andrei Volodin, 2017. "Moment inequalities for m-negatively associated random variables and their applications," Statistical Papers, Springer, vol. 58(3), pages 911-928, September.
    3. Kim, Tae-Sung & Ko, Mi-Hwa & Han, Kwang-Hee, 2008. "On the almost sure convergence for a linear process generated by negatively associated random variables in a Hilbert space," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2110-2115, October.
    4. Zhang, Li-Xin, 2001. "Strassen's law of the iterated logarithm for negatively associated random vectors," Stochastic Processes and their Applications, Elsevier, vol. 95(2), pages 311-328, October.
    5. Mi-Hwa Ko & Tae-Sung Kim & Kwang-Hee Han, 2009. "A Note on the Almost Sure Convergence for Dependent Random Variables in a Hilbert Space," Journal of Theoretical Probability, Springer, vol. 22(2), pages 506-513, June.
    6. Liu, Jingjun & Gan, Shixin & Chen, Pingyan, 1999. "The Hájeck-Rényi inequality for the NA random variables and its application," Statistics & Probability Letters, Elsevier, vol. 43(1), pages 99-105, May.
    7. Cai, Zongwu & Roussas, George G., 1998. "Kaplan-Meier Estimator under Association," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 318-348, November.
    8. Xuejun Wang & Xin Deng & Fengxi Xia & Shuhe Hu, 2017. "The consistency for the estimators of semiparametric regression model based on weakly dependent errors," Statistical Papers, Springer, vol. 58(2), pages 303-318, June.
    9. Allan Gut & Anders Martin-Löf, 2016. "A Maxtrimmed St. Petersburg Game," Journal of Theoretical Probability, Springer, vol. 29(1), pages 277-291, March.
    10. Liang, Han-Ying & Fan, Guo-Liang, 2009. "Berry-Esseen type bounds of estimators in a semiparametric model with linear process errors," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 1-15, January.
    11. Leipus, Remigijus & Paulauskas, Vygantas & Surgailis, Donatas, 2005. "Renewal regime switching and stable limit laws," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 299-327.
    12. Csörgo, Sándor & Simons, Gordon, 2007. "St. Petersburg games with the largest gains withheld," Statistics & Probability Letters, Elsevier, vol. 77(12), pages 1185-1189, July.
    13. Alina Bazarova & István Berkes & Lajos Horváth, 2016. "On the Extremal Theory of Continued Fractions," Journal of Theoretical Probability, Springer, vol. 29(1), pages 248-266, March.
    14. Yanchun Wu & Dawang Wang, 2010. "Almost Sure Convergence of Pair-wise NQD Random Sequence," Modern Applied Science, Canadian Center of Science and Education, vol. 4(12), pages 193-193, December.
    15. Arenal-Gutiérrez, Eusebio & Matrán, Carlos & Cuesta-Albertos, Juan A., 1996. "On the unconditional strong law of large numbers for the bootstrap mean," Statistics & Probability Letters, Elsevier, vol. 27(1), pages 49-60, March.
    16. Bing-Yi Jing & Han-Ying Liang, 2008. "Strong Limit Theorems for Weighted Sums of Negatively Associated Random Variables," Journal of Theoretical Probability, Springer, vol. 21(4), pages 890-909, December.
    17. Debicki, Krzysztof, 1999. "A note on LDP for supremum of Gaussian processes over infinite horizon," Statistics & Probability Letters, Elsevier, vol. 44(3), pages 211-219, September.
    18. Christofides, Tasos C. & Vaggelatou, Eutichia, 2004. "A connection between supermodular ordering and positive/negative association," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 138-151, January.
    19. M. Çağlar, 2004. "A Long-Range Dependent Workload Model for Packet Data Traffic," Mathematics of Operations Research, INFORMS, vol. 29(1), pages 92-105, February.
    20. Zhang, Li-Xin, 2001. "The Weak Convergence for Functions of Negatively Associated Random Variables," Journal of Multivariate Analysis, Elsevier, vol. 78(2), pages 272-298, August.

    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:spr:jotpro:v:34:y:2021:i:1:d:10.1007_s10959-019-00973-2. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.