IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v45y1999i1p85-95.html
   My bibliography  Save this article

Complete convergence for weighted sums of NA sequences

Author

Listed:
  • Liang, Han-Ying
  • Su, Chun

Abstract

Under general weighting coefficient, we obtain the complete convergence for weighted sums of negatively associated (NA) sequences, and discuss its necessity. The results on i.i.d. setting of Chow [Ann. Math. Statist. 37 (1966) 1482-1492], Thrum [Probab. Theory Rel. Fields 75 (1987) 425-430] and Li et al. [J. Theor. Probab. 8 (1995) 49-76] are extended and generalized. Also, the sufficient part of Wang et al.'s [Sci. in China 41 (1998) 939-949] Theorem 1 is extended.

Suggested Citation

  • Liang, Han-Ying & Su, Chun, 1999. "Complete convergence for weighted sums of NA sequences," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 85-95, October.
    • Handle: RePEc:eee:stapro:v:45:y:1999:i:1:p:85-95
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(99)00046-2
    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.

    References listed on IDEAS

    as
    1. Roussas, G. G., 1994. "Asymptotic Normality of Random Fields of Positively or Negatively Associated Processes," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 152-173, July.
    2. 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)

    Citations

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


    Cited by:

    1. Wang, Jiang-Feng & Liang, Han-Ying, 2008. "A note on the almost sure central limit theorem for negatively associated fields," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1964-1970, September.
    2. Qin, Yongsong & Li, Yinghua, 2011. "Empirical likelihood for linear models under negatively associated errors," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 153-163, January.
    3. Kuczmaszewska, Anna, 2009. "On complete convergence for arrays of rowwise negatively associated random variables," Statistics & Probability Letters, Elsevier, vol. 79(1), pages 116-124, January.
    4. 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.
    5. 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.
    6. 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.
    7. Lanzinger, H. & Stadtmüller, U., 2004. "Refined Baum-Katz laws for weighted sums of iid random variables," Statistics & Probability Letters, Elsevier, vol. 69(3), pages 357-368, September.
    8. Han-Ying Liang & Jong-Il Baek, 2008. "Berry–Esseen bounds for density estimates under NA assumption," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 68(3), pages 305-322, November.
    9. Liang, Han-Ying, 2000. "Complete convergence for weighted sums of negatively associated random variables," Statistics & Probability Letters, Elsevier, vol. 48(4), pages 317-325, July.
    10. Yongsong Qin & Yinghua Li & Weizhen Yang & Qingzhu Lei, 2011. "Confidence intervals for nonparametric regression functions under negatively associated errors," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(3), pages 645-659.

    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. 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.
    2. 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.
    3. Liang, Han-Ying & Jing, Bing-Yi, 2005. "Asymptotic properties for estimates of nonparametric regression models based on negatively associated sequences," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 227-245, August.
    4. 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.
    5. Gu, Wentao & Roussas, George G. & Tran, Lanh T., 2007. "On the convergence rate of fixed design regression estimators for negatively associated random variables," Statistics & Probability Letters, Elsevier, vol. 77(12), pages 1214-1224, July.
    6. Zhang, Li-Xin & Wen, Jiwei, 2001. "A weak convergence for negatively associated fields," Statistics & Probability Letters, Elsevier, vol. 53(3), pages 259-267, June.
    7. Liang, Han-Ying, 2000. "Complete convergence for weighted sums of negatively associated random variables," Statistics & Probability Letters, Elsevier, vol. 48(4), pages 317-325, July.
    8. Wang, Jiang-Feng & Liang, Han-Ying, 2008. "A note on the almost sure central limit theorem for negatively associated fields," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1964-1970, September.
    9. Renyu Ye & Xinsheng Liu & Yuncai Yu, 2020. "Pointwise Optimality of Wavelet Density Estimation for Negatively Associated Biased Sample," Mathematics, MDPI, vol. 8(2), pages 1-12, February.
    10. Ming Yuan & Chun Su & Taizhong Hu, 2003. "A Central Limit Theorem for Random Fields of Negatively Associated Processes," Journal of Theoretical Probability, Springer, vol. 16(2), pages 309-323, April.
    11. 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.
    12. Cai, Zongwu & Roussas, George G., 1998. "Kaplan-Meier Estimator under Association," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 318-348, November.
    13. 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.
    14. Shi, Xiaoping & Wu, Yuehua & Miao, Baiqi, 2009. "Strong convergence rate of estimators of change point and its application," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 990-998, February.
    15. Masry, Elias, 2003. "Local polynomial fitting under association," Journal of Multivariate Analysis, Elsevier, vol. 86(2), pages 330-359, August.
    16. 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.
    17. Guodong Xing & Shanchao Yang, 2010. "Some Exponential Inequalities for Positively Associated Random Variables and Rates of Convergence of the Strong Law of Large Numbers," Journal of Theoretical Probability, Springer, vol. 23(1), pages 169-192, March.
    18. 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.
    19. Ioannides, D. A. & Roussas, G. G., 1999. "Exponential inequality for associated random variables," Statistics & Probability Letters, Elsevier, vol. 42(4), pages 423-431, May.
    20. 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.

    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:45:y:1999:i:1:p:85-95. 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/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.