Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2014, Cilt: 43 Sayı: 2, 323 - 335, 01.04.2014

Öz

Kaynakça

  • 1] Hsu, P. L. and Robbins, H. Complete convergence and the law of large numbers. Proc. Natl. Acad. Sci. U.S.A., 33(2), 25–31, 1947.
  • [2] Baum, L. E. and Katz, M. Convergence rates in the law of large numbers. Trans. Am. Math. Soc., 120(1), 108–123, 1965.
  • [3] Liu, L. Precise large deviations for dependent random variables with heavy tails. Statist. Probab. Lett., 79(9), 1290–1298, 2009.
  • [4] Lehmann, E. L. Some concepts of dependence. Ann. Math. Statist., 37(5), 1137–1153, 1966.
  • [5] Joag-Dev, K. and Proschan, F. Negative association of random variables with applications. Ann. Statist., 11(1), 286–295, 1983. 334
  • [6] Shen, A. T. Probability inequalities for END sequence and their applications. J. Inequal. Appl., 2011, 98, 2011.
  • [7] Chen, Y. Q. and Chen, A. Y. and Ng, K. W. The strong law of large numbers for extend negatively dependent random variables. J. Appl. Prob., 47(4), 908–922, 2010.
  • [8] Baek, J. I., Choi, I. B. and Niu, S. l. On the complete convergence of weighted sums for arrays of negatively associated variables. J. Korean Stat. Soc., 37(1), 73–80, 2008.
  • [9] Baek, J. I. and Park, S. T. Convergence of weighted sums for arrays of negatively dependent random variables and its applications. J. Stat. Plan. Infer., 140(9), 2461–2469, 2010.
  • [10] Wu, Q. A complete convergence theorem for weighted sums of arrays of rowwise negatively dependent random variables. J. Inequal. Appl.,2012: 50, 2012.
  • [11] Chow, Y. S. On the rate of moment convergence of sample sums and extremes. Bull. Inst. Math. Acad. Sinica, 16(3), 177–201, 1988.
  • [12] Liang, H. Y., Li, D. L. and Rosalsky, A. Complete moment convergence for sums of negatively associated random variables. Acta Math. Sinica, English Series, 26(3), 419–432, 2010.
  • [13] Sung, S. H. Complete qth moment convergence for arrays of random variables. J. Inequal. Appl., 2013, 24, 2013.
  • [14] Guo, M. L. On complete moment convergence of weighted sums for arrays of row-wise negatively associated random variables. Stochastics: Int. J. Probab. Stoch. Proc., 86(3), 415-428, 2014.
  • [15] Li, Y. X. and Zhang, L. X. Complete moment convergence of moving-average processes under dependence assumptions. Statist. Probab. Lett., 70(3), 191–197, 2004.
  • [16] Wu, Q. Y. Probability Limit Theory for Mixed Sequence. China Science Press, Beijing, 2006.

Complete qth moment convergence of weighted sums for arrays of row-wise extended negatively dependent random variables

Yıl 2014, Cilt: 43 Sayı: 2, 323 - 335, 01.04.2014

Öz

In this paper, the complete qth moment convergence of weighted sums
for arrays of row-wise extended negatively dependent (abbreviated to
END in the following) random variables is investigated. By using
Hoffmann-Jφrgensen type inequality and truncation method, some general results concerning complete qth moment convergence of weighted
sums for arrays of row-wise END random variables are obtained. As
their applications, we extend the corresponding result of Wu (2012) to
the case of arrays of row-wise END random variables. The complete qth
moment convergence of moving average processes based on a sequence
of END random variables is obtained, which improves the result of Li
and Zhang (2004). Moreover, the Baum-Katz type result for arrays of
row-wise END random variables is also obtained.

Kaynakça

  • 1] Hsu, P. L. and Robbins, H. Complete convergence and the law of large numbers. Proc. Natl. Acad. Sci. U.S.A., 33(2), 25–31, 1947.
  • [2] Baum, L. E. and Katz, M. Convergence rates in the law of large numbers. Trans. Am. Math. Soc., 120(1), 108–123, 1965.
  • [3] Liu, L. Precise large deviations for dependent random variables with heavy tails. Statist. Probab. Lett., 79(9), 1290–1298, 2009.
  • [4] Lehmann, E. L. Some concepts of dependence. Ann. Math. Statist., 37(5), 1137–1153, 1966.
  • [5] Joag-Dev, K. and Proschan, F. Negative association of random variables with applications. Ann. Statist., 11(1), 286–295, 1983. 334
  • [6] Shen, A. T. Probability inequalities for END sequence and their applications. J. Inequal. Appl., 2011, 98, 2011.
  • [7] Chen, Y. Q. and Chen, A. Y. and Ng, K. W. The strong law of large numbers for extend negatively dependent random variables. J. Appl. Prob., 47(4), 908–922, 2010.
  • [8] Baek, J. I., Choi, I. B. and Niu, S. l. On the complete convergence of weighted sums for arrays of negatively associated variables. J. Korean Stat. Soc., 37(1), 73–80, 2008.
  • [9] Baek, J. I. and Park, S. T. Convergence of weighted sums for arrays of negatively dependent random variables and its applications. J. Stat. Plan. Infer., 140(9), 2461–2469, 2010.
  • [10] Wu, Q. A complete convergence theorem for weighted sums of arrays of rowwise negatively dependent random variables. J. Inequal. Appl.,2012: 50, 2012.
  • [11] Chow, Y. S. On the rate of moment convergence of sample sums and extremes. Bull. Inst. Math. Acad. Sinica, 16(3), 177–201, 1988.
  • [12] Liang, H. Y., Li, D. L. and Rosalsky, A. Complete moment convergence for sums of negatively associated random variables. Acta Math. Sinica, English Series, 26(3), 419–432, 2010.
  • [13] Sung, S. H. Complete qth moment convergence for arrays of random variables. J. Inequal. Appl., 2013, 24, 2013.
  • [14] Guo, M. L. On complete moment convergence of weighted sums for arrays of row-wise negatively associated random variables. Stochastics: Int. J. Probab. Stoch. Proc., 86(3), 415-428, 2014.
  • [15] Li, Y. X. and Zhang, L. X. Complete moment convergence of moving-average processes under dependence assumptions. Statist. Probab. Lett., 70(3), 191–197, 2004.
  • [16] Wu, Q. Y. Probability Limit Theory for Mixed Sequence. China Science Press, Beijing, 2006.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm İstatistik
Yazarlar

M. L.. Guo Bu kişi benim

Yayımlanma Tarihi 1 Nisan 2014
Yayımlandığı Sayı Yıl 2014 Cilt: 43 Sayı: 2

Kaynak Göster

APA Guo, M. L. (2014). Complete qth moment convergence of weighted sums for arrays of row-wise extended negatively dependent random variables. Hacettepe Journal of Mathematics and Statistics, 43(2), 323-335.
AMA Guo ML. Complete qth moment convergence of weighted sums for arrays of row-wise extended negatively dependent random variables. Hacettepe Journal of Mathematics and Statistics. Nisan 2014;43(2):323-335.
Chicago Guo, M. L. “Complete Qth Moment Convergence of Weighted Sums for Arrays of Row-Wise Extended Negatively Dependent Random Variables”. Hacettepe Journal of Mathematics and Statistics 43, sy. 2 (Nisan 2014): 323-35.
EndNote Guo ML (01 Nisan 2014) Complete qth moment convergence of weighted sums for arrays of row-wise extended negatively dependent random variables. Hacettepe Journal of Mathematics and Statistics 43 2 323–335.
IEEE M. L. Guo, “Complete qth moment convergence of weighted sums for arrays of row-wise extended negatively dependent random variables”, Hacettepe Journal of Mathematics and Statistics, c. 43, sy. 2, ss. 323–335, 2014.
ISNAD Guo, M. L. “Complete Qth Moment Convergence of Weighted Sums for Arrays of Row-Wise Extended Negatively Dependent Random Variables”. Hacettepe Journal of Mathematics and Statistics 43/2 (Nisan 2014), 323-335.
JAMA Guo ML. Complete qth moment convergence of weighted sums for arrays of row-wise extended negatively dependent random variables. Hacettepe Journal of Mathematics and Statistics. 2014;43:323–335.
MLA Guo, M. L. “Complete Qth Moment Convergence of Weighted Sums for Arrays of Row-Wise Extended Negatively Dependent Random Variables”. Hacettepe Journal of Mathematics and Statistics, c. 43, sy. 2, 2014, ss. 323-35.
Vancouver Guo ML. Complete qth moment convergence of weighted sums for arrays of row-wise extended negatively dependent random variables. Hacettepe Journal of Mathematics and Statistics. 2014;43(2):323-35.