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Complete convergence for weighted sums of NA sequences

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  • 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
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    References listed on IDEAS

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    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.
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    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.

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