On complete moment convergence for weighted sums of negatively superadditive dependent random variables

Haiwu Huang; Xuewen Lu

Applications of Mathematics (2020)

  • Volume: 65, Issue: 4, page 355-377
  • ISSN: 0862-7940

Abstract

top
In this work, the complete moment convergence and complete convergence for weighted sums of negatively superadditive dependent (NSD) random variables are studied, and some equivalent conditions of these strong convergences are established. These main results generalize and improve the corresponding theorems of Baum and Katz (1965) and Chow (1988) to weighted sums of NSD random variables without the assumption of identical distribution. As an application, a Marcinkiewicz-Zygmund-type strong law of large numbers for weighted sums of NSD random variables is obtained.

How to cite

top

Huang, Haiwu, and Lu, Xuewen. "On complete moment convergence for weighted sums of negatively superadditive dependent random variables." Applications of Mathematics 65.4 (2020): 355-377. <http://eudml.org/doc/297216>.

@article{Huang2020,
abstract = {In this work, the complete moment convergence and complete convergence for weighted sums of negatively superadditive dependent (NSD) random variables are studied, and some equivalent conditions of these strong convergences are established. These main results generalize and improve the corresponding theorems of Baum and Katz (1965) and Chow (1988) to weighted sums of NSD random variables without the assumption of identical distribution. As an application, a Marcinkiewicz-Zygmund-type strong law of large numbers for weighted sums of NSD random variables is obtained.},
author = {Huang, Haiwu, Lu, Xuewen},
journal = {Applications of Mathematics},
keywords = {NSD random variables; complete moment convergence; weighted sum; equivalent conditions},
language = {eng},
number = {4},
pages = {355-377},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On complete moment convergence for weighted sums of negatively superadditive dependent random variables},
url = {http://eudml.org/doc/297216},
volume = {65},
year = {2020},
}

TY - JOUR
AU - Huang, Haiwu
AU - Lu, Xuewen
TI - On complete moment convergence for weighted sums of negatively superadditive dependent random variables
JO - Applications of Mathematics
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 4
SP - 355
EP - 377
AB - In this work, the complete moment convergence and complete convergence for weighted sums of negatively superadditive dependent (NSD) random variables are studied, and some equivalent conditions of these strong convergences are established. These main results generalize and improve the corresponding theorems of Baum and Katz (1965) and Chow (1988) to weighted sums of NSD random variables without the assumption of identical distribution. As an application, a Marcinkiewicz-Zygmund-type strong law of large numbers for weighted sums of NSD random variables is obtained.
LA - eng
KW - NSD random variables; complete moment convergence; weighted sum; equivalent conditions
UR - http://eudml.org/doc/297216
ER -

References

top
  1. Alam, K., Saxena, K. M. L., 10.1080/03610928108828102, Commun. Stat., Theory Methods A10 (1981), 1183-1196. (1981) Zbl0471.62045MR0623526DOI10.1080/03610928108828102
  2. Amini, M., Bozorgnia, A., Naderi, H., Volodin, A., 10.3103/S1055134415010022, Sib. Adv. Math. 25 (2015), 11-20. (2015) Zbl1328.60082MR3490729DOI10.3103/S1055134415010022
  3. Bai, Z., Su, C., The complete convergence for partial sums of i.i.d. random variables, Sci. Sin., Ser. A 28 (1985), 1261-1277. (1985) Zbl0554.60039MR0851970
  4. Baum, L. E., Katz, M., 10.1090/S0002-9947-1965-0198524-1, Trans. Am. Math. Soc. 120 (1965), 108-123. (1965) Zbl0142.14802MR0198524DOI10.1090/S0002-9947-1965-0198524-1
  5. Chen, P. Y., Wang, D. C., 10.1007/s10114-010-7625-6, Acta Math. Sin., Engl. Ser. 26 (2010), 679-690. (2010) Zbl1205.60062MR2591647DOI10.1007/s10114-010-7625-6
  6. Chow, Y. S., On the rate of moment convergence of sample sums and extremes, Bull. Inst. Math., Acad. Sin. 16 (1988), 177-201. (1988) Zbl0655.60028MR1089491
  7. Christofides, T. C., Vaggelatou, E., 10.1016/S0047-259X(03)00064-2, J. Multivariate Anal. 88 (2004), 138-151. (2004) Zbl1034.60016MR2021866DOI10.1016/S0047-259X(03)00064-2
  8. Deng, X., Wang, X., Wu, Y., Ding, Y., 10.1007/s13398-015-0225-7, Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM 110 (2016), 97-120. (2016) Zbl1334.60037MR3462077DOI10.1007/s13398-015-0225-7
  9. Eghbal, N., Amini, M., Bozorgnia, A., 10.1016/j.spl.2009.12.014, Stat. Probab. Lett. 80 (2010), 587-591. (2010) Zbl1187.60020MR2595134DOI10.1016/j.spl.2009.12.014
  10. Eghbal, N., Amini, M., Bozorgnia, A., 10.1016/j.spl.2011.03.005, Stat. Probab. Lett. 81 (2011), 1112-1120. (2011) Zbl1228.60039MR2803752DOI10.1016/j.spl.2011.03.005
  11. Erdős, P., 10.1214/aoms/1177730037, Ann. Math. Stat. 20 (1949), 286-291. (1949) Zbl0033.29001MR0030714DOI10.1214/aoms/1177730037
  12. Gut, A., 10.1007/978-1-4614-4708-5, Springer Texts in Statistics. Springer, New York (2005). (2005) Zbl1076.60001MR2125120DOI10.1007/978-1-4614-4708-5
  13. Hsu, P. L., Robbins, H., 10.1073/pnas.33.2.25, Proc. Natl. Acad. Sci. USA 33 (1947), 25-31. (1947) Zbl0030.20101MR0019852DOI10.1073/pnas.33.2.25
  14. Hu, T., Negatively superadditive dependence of random variables with applications, Chin. J. Appl. Probab. Stat. 16 (2000), 133-144. (2000) Zbl1050.60502MR1812714
  15. Joag-Dev, K., Proschan, F., 10.1214/aos/1176346079, Ann. Stat. 11 (1983), 286-295. (1983) Zbl0508.62041MR0684886DOI10.1214/aos/1176346079
  16. Kemperman, J. H. B., 10.1016/1385-7258(77)90027-0, Nederl. Akad. Wet., Proc., Ser. A 80 (1977), 313-331. (1977) Zbl0384.28012MR0467867DOI10.1016/1385-7258(77)90027-0
  17. Naderi, H., Amini, M., Bozorgnia, A., 10.1007/s11766-017-3437-0, Appl. Math., Ser. B (Engl. Ed.) 32 (2017), 270-280. (2017) Zbl1399.60053MR3694062DOI10.1007/s11766-017-3437-0
  18. Shen, Y., Wang, X. J., Yang, W. Z., Hu, S. H., 10.1007/s10114-012-1723-6, Acta Math. Sin., Engl. Ser. 29 (2013), 743-756. (2013) Zbl1263.60025MR3029287DOI10.1007/s10114-012-1723-6
  19. Shen, A., Xue, M., Volodin, A., 10.1080/17442508.2015.1110153, Stochastics 88 (2016), 606-621. (2016) Zbl1337.60038MR3473853DOI10.1080/17442508.2015.1110153
  20. Shen, A., Zhang, Y., Volodin, A., 10.1007/s00184-014-0503-y, Metrika 78 (2015), 295-311. (2015) Zbl1333.60022MR3320899DOI10.1007/s00184-014-0503-y
  21. Sung, S. H., 10.1155/2009/271265, J. Inequal. Appl. 2009 (2009), Article ID 271265, 14 pages. (2009) Zbl1180.60019MR2551753DOI10.1155/2009/271265
  22. Wang, X., Deng, X., Zheng, L., Hu, S., 10.1080/02331888.2013.800066, Statistics 48 (2014), 834-850. (2014) Zbl1319.60063MR3234065DOI10.1080/02331888.2013.800066
  23. Wang, X., Shen, A., Chen, Z., Hu, S., 10.1007/s11749-014-0402-6, TEST 24 (2015), 166-184. (2015) Zbl1316.60042MR3314578DOI10.1007/s11749-014-0402-6
  24. Wang, X., Wu, Y., 10.4134/JKMS.j160293, J. Korean Math. Soc. 54 (2017), 877-896. (2017) Zbl1366.60068MR3640914DOI10.4134/JKMS.j160293
  25. Wu, Q., Probability Limit Theory for Mixing Sequences, Science Press of China, Beijing (2006). (2006) 
  26. Wu, Y., 10.1007/s13398-013-0133-7, Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM 108 (2014), 669-681. (2014) Zbl1296.60078MR3249968DOI10.1007/s13398-013-0133-7
  27. Zhang, Y., 10.2298/FIL1507541Z, Filomat 29 (2015), 1541-1547. (2015) Zbl06749122MR3373155DOI10.2298/FIL1507541Z
  28. Zheng, L., Wang, X., Yang, W., 10.2298/FIL1702295Z, Filomat 31 (2017), 295-308. (2017) MR3628840DOI10.2298/FIL1702295Z
  29. Zhou, X., 10.1016/j.spl.2009.10.018, Stat. Probab. Lett. 80 (2010), 285-292. (2010) Zbl1186.60031MR2593564DOI10.1016/j.spl.2009.10.018

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.