Publication Cover
Statistics
A Journal of Theoretical and Applied Statistics
Volume 57, 2023 - Issue 3
117
Views
1
CrossRef citations to date
0
Altmetric
Research Article

Some improved results on Berry–Esséen bounds for strong mixing random variables and applications

, , &
Pages 740-760 | Received 02 Sep 2022, Accepted 08 May 2023, Published online: 17 May 2023

References

  • Petrov VV. Limit theorems of probability theory. New York: Oxford University. Press Inc.; 1995.
  • Shiryaev AN. Probability. 2nd ed., New York Inc: Springer-Verlag; 1996.
  • Chanda KC. Strong mixing properties of linear processes. J Appl Probab. 1974;11:401–408.
  • Gorodetskii VV. On the strong mixing properties for linear processes. Theory Probab Appl. 1977;22:413–441.
  • Withers CS. Conditions for linear processes to be strong mixing. Z Wahrsch Verw Gebiete. 1981;57(4):477–480.
  • Pham TD, Tran LT. Some strong mixing properties of time series models. Stoch Process Their Appl. 1985;19:297–303.
  • Genon-Catahot V, Jeantheau T, Laredo C. Stochastic volatility models as hidden Markov models and applications. Bernoulli. 2000;6(6):1051–1079.
  • Rosenblatt M. A central limit theorem and a strong mixing condition. Proc Natl Acad Sci USA. 1956;42:43–47.
  • Lahiri SN, Sun S. A Berry-Esséen theorem for sample quantiles under weak dependent. Ann Appl Probab. 2009;19(1):108–126.
  • Yang WZ, Hu SH, Wang XJ, et al. The Berry-Esséen type bound of sample quantiles for strong mixing sequence. J Stat Plan Inference. 2012;142:660–672.
  • Bahadur RR. A note on quantiles in large samples. Ann Math Stat. 1966;37(3):577–580.
  • Sen PK. On Bahadur representation of sample quantile for sequences of ϕ-mixing random variables. J Multivar Anal. 1972;2(1):77–95.
  • Yoshihara K. The Bahadur representation of sample quantile for sequences of strongly mixing random variables. Stat Probab Lett. 1995;24(4):299–304.
  • Sun SX. The Bahadur representation for sample quantiles under weak dependence. Stat Probab Lett. 2006;76(12):1238–1244.
  • Ling NX. The Bahadur representation for sample quantiles under negatively associated sequence. Stat Probab Lett. 2008;78(16):2660–2663.
  • Wei X, Yang SC, Yu KM, et al. Bahadur representation of linear kernel quantile estimator of var under α-mixing assumption. J Stat Plan Inference. 2010;140(7):1620–1634.
  • Yang WZ, Liu TT, Wang XJ, et al. On the Bahadur representation of sample quantiles for widely orthant dependent sequences. Filomat. 2014;28(7):1333–1343.
  • Wang XJ, Hu SH. The Berry-Esseen bound for α-mixing random variables and its applications in nonparametric regression model. Theory Probab Appl. 2019;63:479–499.
  • Wang XJ, Wu Y, Yu W, et al. Asymptotics for the linear kernel quantile estimator of value-at-risk. TEST. 2019;28(4):1144–1174.
  • Yang SC. Maximal moment inequality for partial sums of strong mixing sequences and application. Acta Math Sin Engl Ser. 2007;23(6):1013–1024.
  • Hall P, Heyde CC. Martingale limit theory and its application. New York: Academic Press, Inc.; 1980.
  • Yang SC, Li YM. Uniformly asymptotic normality of the regression weighted estimator for α-mixing samples. Acta Math Sin Chinese Ser. 2006;49:1163–1170.
  • Liang HY, Fan GL. Berry-Esséen type bounds of estimators in a semiparametric model with linear process errors. J Multivar Anal. 2009;100:1–15.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.