Convergence properties for arrays of rowwise pairwise negatively quadrant dependent random variables

Yongfeng Wu; Dingcheng Wang

Applications of Mathematics (2012)

  • Volume: 57, Issue: 5, page 463-476
  • ISSN: 0862-7940

Abstract

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In this paper the authors study the convergence properties for arrays of rowwise pairwise negatively quadrant dependent random variables. The results extend and improve the corresponding theorems of T. C. Hu, R. L. Taylor: On the strong law for arrays and for the bootstrap mean and variance, Int. J. Math. Math. Sci 20 (1997), 375–382.

How to cite

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Wu, Yongfeng, and Wang, Dingcheng. "Convergence properties for arrays of rowwise pairwise negatively quadrant dependent random variables." Applications of Mathematics 57.5 (2012): 463-476. <http://eudml.org/doc/246496>.

@article{Wu2012,
abstract = {In this paper the authors study the convergence properties for arrays of rowwise pairwise negatively quadrant dependent random variables. The results extend and improve the corresponding theorems of T. C. Hu, R. L. Taylor: On the strong law for arrays and for the bootstrap mean and variance, Int. J. Math. Math. Sci 20 (1997), 375–382.},
author = {Wu, Yongfeng, Wang, Dingcheng},
journal = {Applications of Mathematics},
keywords = {complete convergence; complete moment convergence; $L^q$ convergence; pairwise NQD random variables; complete convergence; complete moment convergence; convergence; pairwise NQD random variables},
language = {eng},
number = {5},
pages = {463-476},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Convergence properties for arrays of rowwise pairwise negatively quadrant dependent random variables},
url = {http://eudml.org/doc/246496},
volume = {57},
year = {2012},
}

TY - JOUR
AU - Wu, Yongfeng
AU - Wang, Dingcheng
TI - Convergence properties for arrays of rowwise pairwise negatively quadrant dependent random variables
JO - Applications of Mathematics
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 5
SP - 463
EP - 476
AB - In this paper the authors study the convergence properties for arrays of rowwise pairwise negatively quadrant dependent random variables. The results extend and improve the corresponding theorems of T. C. Hu, R. L. Taylor: On the strong law for arrays and for the bootstrap mean and variance, Int. J. Math. Math. Sci 20 (1997), 375–382.
LA - eng
KW - complete convergence; complete moment convergence; $L^q$ convergence; pairwise NQD random variables; complete convergence; complete moment convergence; convergence; pairwise NQD random variables
UR - http://eudml.org/doc/246496
ER -

References

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  1. Adler, A., Rosalsky, A., Volodin, A., 10.1016/S0167-7152(97)85593-9, Stat. Probab. Lett. 32 (1997), 167-174. (1997) Zbl0874.60008MR1436862DOI10.1016/S0167-7152(97)85593-9
  2. Bryc, W., Smoleński, W., 10.1090/S0002-9939-1993-1149969-7, Proc. Am. Math. Soc. 119 (1993), 629-635. (1993) Zbl0785.60018MR1149969DOI10.1090/S0002-9939-1993-1149969-7
  3. Chow, Y. S., On the rate of moment complete convergence of sample sums and extremes, Bull. Inst. Math. Acad. Sin. 16 (1988), 177-201. (1988) MR1089491
  4. Ebrahimi, N., Ghosh, M., 10.1080/03610928108828041, Commun. Stat., Theory Methods 10 (1981), 307-337. (1981) Zbl0506.62034MR0612400DOI10.1080/03610928108828041
  5. Gan, S. X., Chen, P. Y., 10.1016/S0252-9602(07)60027-7, Acta Math. Sci., Ser. B, Engl. Ed. 27 (2007), 283-290. (2007) Zbl1125.60027MR2313226DOI10.1016/S0252-9602(07)60027-7
  6. Hsu, P. L., Robbins, H., 10.1073/pnas.33.2.25, Proc. Natl. Acad. Sci. 33 (1947), 25-31. (1947) Zbl0030.20101MR0019852DOI10.1073/pnas.33.2.25
  7. Hu, T. C., Taylor, R. L., 10.1155/S0161171297000483, Int. J. Math. Math. Sci. 20 (1997), 375-382. (1997) Zbl0883.60024MR1444739DOI10.1155/S0161171297000483
  8. Joag-Dev, K., Proschan, F., 10.1214/aos/1176346079, Ann. Stat. 11 (1983), 286-295. (1983) MR0684886DOI10.1214/aos/1176346079
  9. Lehmann, E. L., 10.1214/aoms/1177699260, Ann. Math. Stat. 37 (1966), 1137-1153. (1966) Zbl0146.40601MR0202228DOI10.1214/aoms/1177699260
  10. Wang, D. C., Zhao, W., Moment complete convergence for sums of a sequence of NA random variables, Appl. Math., Ser. A (Chin. Ed.) 21 (2006), 445-450 Chinese. (2006) Zbl1137.60320MR2270685
  11. Wu, Q. Y., Convergence properties of pairwise NQD random sequences, Acta Math. Sin. 45 (2002), 617-624 Chinese. (2002) Zbl1008.60039MR1915127
  12. Wu, Y. F., Zhu, D. J., 10.1016/j.jkss.2009.05.003, J. Korean Stat. Soc. 39 (2010), 189-197 2642485. (2010) Zbl1294.60056MR2642485DOI10.1016/j.jkss.2009.05.003
  13. Yang, S. C., Almost sure convergence of weighted sums of mixing sequences, J. Syst. Sci. Math. Sci. 15 (1995), 254-265 Chinese. (1995) Zbl0869.60029

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