Complete -moment convergence for weighted sums of WOD arrays with statistical applications

Xi Chen; Xinran Tao; Xuejun Wang

Kybernetika (2023)

  • Volume: 59, Issue: 1, page 1-27
  • ISSN: 0023-5954

Abstract

top
Complete -moment convergence is much more general than complete convergence and complete moment convergence. In this work, we mainly investigate the complete -moment convergence for weighted sums of widely orthant dependent (WOD, for short) arrays. A general result on Complete -moment convergence is obtained under some suitable conditions, which generalizes the corresponding one in the literature. As an application, we establish the complete consistency for the weighted linear estimator in nonparametric regression models. Finally, some simulations are provided to show the numerical performance of theoretical results based on finite samples.

How to cite

top

Chen, Xi, Tao, Xinran, and Wang, Xuejun. "Complete $f$-moment convergence for weighted sums of WOD arrays with statistical applications." Kybernetika 59.1 (2023): 1-27. <http://eudml.org/doc/299075>.

@article{Chen2023,
abstract = {Complete $f$-moment convergence is much more general than complete convergence and complete moment convergence. In this work, we mainly investigate the complete $f$-moment convergence for weighted sums of widely orthant dependent (WOD, for short) arrays. A general result on Complete $f$-moment convergence is obtained under some suitable conditions, which generalizes the corresponding one in the literature. As an application, we establish the complete consistency for the weighted linear estimator in nonparametric regression models. Finally, some simulations are provided to show the numerical performance of theoretical results based on finite samples.},
author = {Chen, Xi, Tao, Xinran, Wang, Xuejun},
journal = {Kybernetika},
keywords = {widely orthant dependent arrays; weighted sums; complete $f$-moment convergence; complete convergence; nonparametric regression models; complete consistency},
language = {eng},
number = {1},
pages = {1-27},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Complete $f$-moment convergence for weighted sums of WOD arrays with statistical applications},
url = {http://eudml.org/doc/299075},
volume = {59},
year = {2023},
}

TY - JOUR
AU - Chen, Xi
AU - Tao, Xinran
AU - Wang, Xuejun
TI - Complete $f$-moment convergence for weighted sums of WOD arrays with statistical applications
JO - Kybernetika
PY - 2023
PB - Institute of Information Theory and Automation AS CR
VL - 59
IS - 1
SP - 1
EP - 27
AB - Complete $f$-moment convergence is much more general than complete convergence and complete moment convergence. In this work, we mainly investigate the complete $f$-moment convergence for weighted sums of widely orthant dependent (WOD, for short) arrays. A general result on Complete $f$-moment convergence is obtained under some suitable conditions, which generalizes the corresponding one in the literature. As an application, we establish the complete consistency for the weighted linear estimator in nonparametric regression models. Finally, some simulations are provided to show the numerical performance of theoretical results based on finite samples.
LA - eng
KW - widely orthant dependent arrays; weighted sums; complete $f$-moment convergence; complete convergence; nonparametric regression models; complete consistency
UR - http://eudml.org/doc/299075
ER -

References

top
  1. Adler, A., Rosalsky, A., , Stoch. Anal. Appl. 5 (1987), 1-16. Zbl0617.60028MR0882694DOI
  2. Adler, A., Rosalsky, A., Taylor, R. L., 10.1155/S0161171289000657, Int. J. Math. Math. Sci. 12 (1989), 507-530. MR1007204DOI10.1155/S0161171289000657
  3. Chen, P. Y., Sung, S. H., , Statist. Probab. Lett. 2054 (2019), 1-8, Article ID 108544. MR3980503DOI
  4. Chow, Y. S., On the rate of moment convergence of sample sums and extremes., Bull. Inst. Math., Academia Sinica 16 (1988), 177-201. MR1089491
  5. Georgiev, A. A., Local properties of function fitting estimates with applications to system identification., In: Mathematics Statistics and Applications. Proceedings 4th Pannonian Symposium on Mathematical Statistics 1983, (W. Grossmann, ed.). vol. B, Bad Tatzmannsdorf, Austria, Reidel, Dordrecht, pp. 141-51. MR0851050
  6. Georgiev, A. A., Greblicki, W., , J. Statist. Plann. Inference 13 (1986), 1-14. MR0822121DOI
  7. He, Q. H., , J. Inequal. Appl. 2019 (2019), 1-13, Article ID 64. MR3923002DOI
  8. Hsu, P. L., Robbins, H., , Proc. National Acad. Sci. Unit. States Amer. 33 (1947), 25-31. Zbl0030.20101MR0019852DOI
  9. Joag-Dev, K., Proschan, F., , Ann. Statist. 11 (1983), 286-295. MR0684886DOI
  10. Lang, J. J., He, T. Y., Cheng, L., Lu, C., Wang, X. J., , Revista Mat. Complut. 34 (2021), 853-881. MR4302244DOI
  11. Li, Y. M., Zhou, Y., Liu, C., , J. Inequal. Appl. 2018 (2018), 1-10, Article ID 71. MR3782674DOI
  12. Liang, H. Y., Jing, B. Y., , J. Multivar. Anal. 95 (2005), 227-245. MR2170396DOI
  13. Liang, H. Y., Zhang, J. J., , Chinese Annals of Mathematics 31B (2010), 273-288. MR2607650DOI
  14. Lu, C., Chen, Z., Wang, X. J., , Acta Math. Sinica, English Series 35 (2019), 1917-1936. MR4033590DOI
  15. Hu, D. H. Qiu abd T. C., Strong limit theorems for weighted sums of widely orthant dependent random variables., J. Math. Res. Appl. 34 (2014), 105-113. MR3220656
  16. Qiu, D. H., Chen, P. Y., , Acta Math. Sinica, English Series 30 (2014), 1539-1548. MR3245935DOI
  17. Roussas, G. G., Tran, L. T., Ioannides, D. A., , J. Multivar. Anal. 40 (1992), 262-291. MR1150613DOI
  18. Shen, A.T., , J. Nonparametr. Statist. 28 (2016), 702-715. MR3555453DOI
  19. Shen, A. T., Wu, C. Q., Complete th moment convergence and its statistical applications., RACSAM 114 (2019), 1-25, Article ID 35. MR4042305
  20. Shen, A. T., Yao, M., Wang, W. J., Volodin, A., , RACSAM 110 (2016), 251-268. MR3462086DOI
  21. Shen, A. T., Zhang, S. Y., , Methodol. Comput. Appl. Probab. 23 (2021), 1285-1307. MR4335161DOI
  22. Shen, A. T., Zhang, Y., Volodin, A., , Metrika 78 (2015), 295-311. MR3320899DOI
  23. Stout, W. F., Almost Sure Convergence., Academic Press, New York 1974. MR0455094
  24. Stone, C. J., 10.1214/aos/1176343886, Ann. Statist. 5 (1977), 595-620. MR0443204DOI10.1214/aos/1176343886
  25. Tran, L., Roussas, G., Yakowitz, S., Truong, V. B., , Ann. Statist. 24 (1996), 975-991. MR1401833DOI
  26. Wang, Y., Wang, X. J., , Statist. Papers 62 (2021), 769-793. MR4232917DOI
  27. Wang, K. Y., Wang, Y. B., Gao, Q. W., , Methodol. Comput. Appl. Probab. 15 (2013), 109-124. MR3030214DOI
  28. Xi, M. M., Wang, R., Cheng, Z. Y., Wang, X. J., , Statist. Papers 61 (2020), 1663-1684. MR4127491DOI
  29. Wu, Q. Y., Probability Limit Theory for Mixing Sequences., Science Press of China, Beijing 2006. 
  30. Wu, Y., Wang, X. J., Hu, S. H., , Statist. Probab. Lett. 127 (2017), 56-66. MR3648295DOI
  31. Wu, Y., Wang, X. J., Hu, T. C., Volodin, A., 10.1007/s13398-017-0480-x, RACSAM 113 (2019), 333-351. MR3942340DOI10.1007/s13398-017-0480-x
  32. Wu, Y., Wang, X. J., Rosalsky, A., , Acta Math. Sinica, English Series 34 (2018), 1531-1548. MR3854379DOI
  33. Wu, Y., Wang, X. J., Shen, A. T., , Statist. Papers 62 (2021), 2169-94. MR4314255DOI
  34. Yang, W. Z., Xu, H. Y., Chen, L., Hu, aand S. H., , Statist. Papers 59 (2018), 449-465. MR3800809DOI
  35. Zhang, S. L., Qu, C., Hou, T. T., , Commun. Statist. - Theory Methods, 2022, in press. MR4198622DOI
  36. Zhou, X. C., Lin, J. G., Yin, C. M., , J. Inequal. Appl. 2013 (2013), 1-18, Article ID 261. MR3068636DOI
  37. Wang, X. J., Xu, C., Hu, T. C., Volodin, A., Hu, S. H., , TEST 23 (2014), 607-629. MR3252097DOI

NotesEmbed ?

top

You must be logged in to post comments.