| Title:
|
Convergence properties for arrays of rowwise pairwise negatively quadrant dependent random variables (English) |
| Author:
|
Wu, Yongfeng |
| Author:
|
Wang, Dingcheng |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
57 |
| Issue:
|
5 |
| Year:
|
2012 |
| Pages:
|
463-476 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
complete convergence |
| Keyword:
|
complete moment convergence |
| Keyword:
|
$L^q$ convergence |
| Keyword:
|
pairwise NQD random variables |
| MSC:
|
60F15 |
| MSC:
|
60F25 |
| idZBL:
|
Zbl 1265.60067 |
| idMR:
|
MR2984614 |
| DOI:
|
10.1007/s10492-012-0027-6 |
| . |
| Date available:
|
2012-08-19T21:57:54Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142911 |
| . |
| Reference:
|
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| Reference:
|
[2] Bryc, W., Smoleński, W.: Moment conditions for almost sure convergence of weakly correlated random variables.Proc. Am. Math. Soc. 119 (1993), 629-635. Zbl 0785.60018, MR 1149969, 10.1090/S0002-9939-1993-1149969-7 |
| Reference:
|
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| Reference:
|
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| Reference:
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[5] Gan, S. X., Chen, P. Y.: On the limiting behavior of the maximum partial sums for arrays of rowwise NA random variables.Acta Math. Sci., Ser. B, Engl. Ed. 27 (2007), 283-290. Zbl 1125.60027, MR 2313226, 10.1016/S0252-9602(07)60027-7 |
| Reference:
|
[6] Hsu, P. L., Robbins, H.: Complete convergence and the law of large numbers.Proc. Natl. Acad. Sci. 33 (1947), 25-31. Zbl 0030.20101, MR 0019852, 10.1073/pnas.33.2.25 |
| Reference:
|
[7] Hu, T. C., Taylor, R. L.: On the strong law for arrays and for the bootstrap mean and variance.Int. J. Math. Math. Sci. 20 (1997), 375-382. Zbl 0883.60024, MR 1444739, 10.1155/S0161171297000483 |
| Reference:
|
[8] Joag-Dev, K., Proschan, F.: Negative association of random variables with applications.Ann. Stat. 11 (1983), 286-295. MR 0684886, 10.1214/aos/1176346079 |
| Reference:
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[9] Lehmann, E. L.: Some concepts of dependence.Ann. Math. Stat. 37 (1966), 1137-1153. Zbl 0146.40601, MR 0202228, 10.1214/aoms/1177699260 |
| Reference:
|
[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. Zbl 1137.60320, MR 2270685 |
| Reference:
|
[11] Wu, Q. Y.: Convergence properties of pairwise NQD random sequences.Acta Math. Sin. 45 (2002), 617-624 Chinese. Zbl 1008.60039, MR 1915127 |
| Reference:
|
[12] Wu, Y. F., Zhu, D. J.: Convergence properties of partial sums for arrays of rowwise negatively orthant dependent random variables.J. Korean Stat. Soc. 39 (2010), 189-197 \MR 2642485. Zbl 1294.60056, MR 2642485, 10.1016/j.jkss.2009.05.003 |
| Reference:
|
[13] Yang, S. C.: Almost sure convergence of weighted sums of mixing sequences.J. Syst. Sci. Math. Sci. 15 (1995), 254-265 Chinese. Zbl 0869.60029 |
| . |
