References
- Bradley RC. On the spectral density and asymptotic normality of weakly dependent random fields. J Theor Probab. 1992;5:355–373. doi: 10.1007/BF01046741
- Utev S, Peligrad M. Maximal inequalities and an invariant principle for a class of weakly dependent random variables. J Theor Probab. 2003;16:101–115. doi: 10.1023/A:1022278404634
- Choi JY, Baek JI. On the Hajeck-Renyi-type inequality for ρ~-mixing sequence. Honam Math J. 2008;30:479–486. doi: 10.5831/HMJ.2008.30.3.479
- Kuczmaszewska A. On Chung-Teicher type strong law of large numbers for ρ∗-mixing random variables. Discrete Dyn Nat Soc. 2008;2008: Article ID 140548, 10 pages. doi: 10.1155/2008/140548
- Wu QY, Jiang YY. Some strong limit theorems for ρ~-mixing sequence of random variables. Statist Probab Lett. 2008;78:1017–1023. doi: 10.1016/j.spl.2007.09.061
- Sung SH. Complete qth moment convergence for arrays of random variables. J Inequ Appl. 2013;2013: Article ID 24, 11 pages.
- Luo ZD, Yang SC. The asymptotic properties of CVaR estimator under ρ~-mixing sequence. Acta Math Sin. 2013;56:851–870.
- Wu Y, Wang XJ, Hu SH. Complete moment convergence for weighted sums of weakly dependent random variables and its application in nonparametric regression model. Statist Probab Lett. 2017;127:56–66. doi: 10.1016/j.spl.2017.03.027
- Chen PY, Sung SH. On complete convergence and complete moment convergence for weighted sums of ρ∗-mixing random variables. J Inequ Appl. 2018;2018: Article ID 121, 16 pages.
- Bai ZD, Chen PE. Marcinkiewicz strong laws for linear statistics. Statist Probab Lett. 2000;46:105–112. doi: 10.1016/S0167-7152(99)00093-0
- Sung SH. Complete convergence for weighted sums of random variables. Statist Probab Lett. 2007;77:303–311. doi: 10.1016/j.spl.2006.07.010
- Chen PY, Ma XF, Sung SH. On complete convergence and strong law for weighted sums of i.i.d. random variables. Abstr Appl Anal. 2014; 2014:Article ID 251435, 7 pages.
- Chow YS. On the rate of moment convergence of sample sums and extremes. Bulletin of the Institute of Mathematics, Academia Sinica, 1988;16:177–201.
- Hsu PL, Robbins H. Complete convergence and the laws of large numbers. Proc Natl Acad Sci USA. 1947;33:25–31. doi: 10.1073/pnas.33.2.25
- Zhou XC, Lin JG. Complete qth moment convergence of moving average processes under ϕ-mixing assumption. Math Slovaca. 2011;6:979–992.
- Qiu DH, Chen PY. Complete and complete moment convergence for weighted sums of widely orthant dependent random variables. Acta Mathematica Sinica, English Series. 2014;30:1539–1548. doi: 10.1007/s10114-014-3483-y
- Wu YF. On complete moment convergence for arrays of rowwise negatively associated random variables. RACSAM. 2014;108:669–681. doi: 10.1007/s13398-013-0133-7
- Masuda H, Shimizu Y. Moment convergence in regularized estimation under multiple and mixed-rates asymptotics. Mathematical Methods of Statistics, 2017;26:81–110. doi: 10.3103/S1066530717020016
- Ko MH. On complete moment convergence for CAANA random vectors in Hilbert spaces. Statist Probab Lett. 2018;138:104–110. doi: 10.1016/j.spl.2018.02.068
- Seneta E. Regularly varying function. Publ Inst Math. 2013;508:195–211.
- Wu QY. Probability limit theory for mixing sequences. Beijing: Science Press of China; 2006.
- Shen AT, Zhang Y, Volodin A. Applications of the Rosenthal-type inequality for negatively superadditive dependent random variables. Metrika. 2015;78:295–311. doi: 10.1007/s00184-014-0503-y
- Ogata K. Modern control engineering. 4th ed. Englewood Cliffs (NJ): Prentice-Hall; 2002.
- Thanh LV, Yin GG, Wang LY. State observers with random sampling times and convergence analysis of double-indexed and randomly weighted sums of mixing processes. SIAM J Control Optim. 2011;49:106–124. doi: 10.1137/10078671X
- Wang LY, Li C, Yin G, et al. State observability and observers of linear-time-invariant systems under irregular smpling and sensor limitations. IEEE Trans Automat Contr. 2011;56:2639–2654. doi: 10.1109/TAC.2011.2122570
- Wang XJ, Wu Y, Hu SH. Complete moment convergence for double-indexed randomly weighted sums and its applications. Statistics. 2018;52:503–518. doi: 10.1080/02331888.2018.1436548
- Stone CJ. Consistent nonparametric regression regression. Ann Statist. 1977;5:595–620. doi: 10.1214/aos/1176343886
- Roussas GG, Tran LT, Ioannides DA. Fixed design regression for time series: asymptotic normality. J Multivar Anal. 1992;40:262–291. doi: 10.1016/0047-259X(92)90026-C
- Tran LT, Roussas GG, Yakowitz S, et al. Fixed design regression for linear time serries. Ann Statist. 1996;24:975–991. doi: 10.1214/aos/1032526952
- Wang XJ, Xu C, Hu TC, et al. On complete convergence for widely orthant-dependent random variables and its applications in nonparametric regression models. TEST. 2014;23:607–629. doi: 10.1007/s11749-014-0365-7
- Wang XJ, Si ZY. Complete consistency of the estimator of nonparametric regression model under ND sequence. Statist Papers. 2015;56:585–596. doi: 10.1007/s00362-014-0598-2
- Liang HY, Baek JJ. Asymptotic normality of conditional density estimation with left-truncated and dependent data. Statist Papers. 2016;57:1–20. doi: 10.1007/s00362-014-0635-1
- Shen AT. Complete convergence for weighted sums of END random variables and its application to nonparametric regression models. J Nonparametr Stat. 2016;28:702–715. doi: 10.1080/10485252.2016.1225050
- Shen AT, Yao M, Wang WJ, et al. Exponential probability inequalities for WNOD random variables and their applications. RACSAM. 2016;110:251–268. doi: 10.1007/s13398-015-0233-7
- Yang WZ, Xu HY, Chen L, et al. Complete consistency of estimators for regression models based on extended negatively dependent. Statist Papers. 2018;59:449–465. doi: 10.1007/s00362-016-0771-x
- Lu C, Chen Z, Wang XJ. Complete f-moment convergence for widely orthant dependent random variables and its application in nonparametric models. Acta Math Sin Engl Ser. 2019;35:1917–1936. doi: 10.1007/s10114-019-8315-7
- Wieczorek B, Ziegler K. On optimal estimation of a non-smooth mode in a nonparametric regression model with α-mixing errors. J Stat Plan Inference. 2010;140:406–418. doi: 10.1016/j.jspi.2009.07.016