References
- A. Adler and A. Rosalsky, Some general strong laws for weighted sums of stochastically dominated random variables, Stoch. Anal. Appl. 5(1) (1987), pp. 1–16. doi: 10.1080/07362998708809104
- A. Adler, A. Rosalsky, and R.L. Taylor, Strong laws of large numbers for weighted sums of random elements in normed linear spaces, Int. J. Math. Math. Sci. 12 (1989), pp. 507–529. doi: 10.1155/S0161171289000657
- P.Y. Chen, Limiting behavior of weighted sums of negatively associated random variables, Acta Math. Sci. 25(4) (2005), pp. 489–495. doi: 10.1016/S0252-9602(17)30204-7
- Y. Chen, L. Wang, and Y.B. Wang, Uniform asymptotics for the finite-time ruin probabilities of two kinds of nonstandard bidimensional risk models, J. Math. Anal. Appl. 401 (2013), pp. 114–129. doi: 10.1016/j.jmaa.2012.11.046
- Y.S. Chow, Some convergence theorems for independent random variables, Ann. Math. Stat. 37 (1966), pp. 1482–1493. doi: 10.1214/aoms/1177699140
- X. Deng and X.J. Wang, An exponential inequality and its application to M estimators in multiple linear models, Statist. Papers (2018). Available at https://doi.org/10.1007/s00362-018-0994-0, in press.
- Y. Fan, Consistent nonparametric multiple regression for dependent heterogeneous processes, J. Multivariate Anal. 33(1) (1990), pp. 72–88. doi: 10.1016/0047-259X(90)90006-4
- A.A. Georgiev, Local properties of function fitting estimates with application to system identification, in Mathematical Statistics and Applications, W. Grossmann et al., eds., Proceedings 4th Pannonian Sump. Math. Statist. 4–10 September 1983, Bad Tatzmannsdorf, Austria, Reidel, Dordrecht, 1985, pp. 141–151.
- A.A. Georgiev and W. Greblicki, Nonparametric function recovering from noisy observations, J. Statist. Plann. Inference 13(1) (1986), pp. 1–14. doi: 10.1016/0378-3758(86)90114-X
- P.L. Hsu and H. Robbins, Complete convergence and the law of large numbers, Proc. Nat. Acad. Sci. U.S.A. 33(2) (1947), pp. 25–31. doi: 10.1073/pnas.33.2.25
- T.Z. Hu, Negatively superadditive dependence of random variables with applications, Chinese J. Appl. Probab. Stat. 16 (2000), pp. 133–144.
- K. Joag-Dev and F. Proschan, Negative association of random variables with applications, Ann. Stat. 11 (1983), pp. 286–295. doi: 10.1214/aos/1176346079
- X.Q. Li, X. Liu, W.Z. Yang, and S.H. Hu, The inverse moment for widely orthant dependent random variables, J. Ineq. Appl. 2016 (2016), p. 11. Article ID 161. doi: 10.1186/s13660-015-0941-8
- H.Y. Liang and B.Y. Jing, Asymptotic properties for estimates of nonparametric regression models based on negatively associated sequences, J. Multivariate Anal. 95 (2005), pp. 227–245. doi: 10.1016/j.jmva.2004.06.004
- L. Liu, Precise large deviations for dependent random variables with heavy tails, Statist. Probab. Lett. 79(9) (2009), pp. 1290–1298. doi: 10.1016/j.spl.2009.02.001
- H.G. Müller, Weak and universal consistency of moving weighted averages, Period. Math. Hungar. 18(3) (1987), pp. 241–250. doi: 10.1007/BF01848087
- H.R. Nili Sani, M. Amini, and A. Bozorgnia, Strong laws for weighted sums of negative dependent random variables. Islamic Republic of Iran, J. Sci. 16(3) (2005), pp. 261–266.
- M.M. Ning, C.Q. Wu, and A.T. Shen, Complete convergence of weighted sums of WNOD random variables and its applications, Stochastics 92(1) (2020), pp. 24–45. doi: 10.1080/17442508.2019.1595623
- D.H. Qiu and P.Y. Chen, Complete and complete moment convergence for weighted sums of widely orthant dependent random variables, Acta Math. Sinica 30(9) (2014), pp. 1539–1548. doi: 10.1007/s10114-014-3483-y
- D.H. Qiu and T.C. Hu, Strong limit theorems for weighted sums of widely orthant dependent random variables, J. Math. Res. Appl. 34(1) (2014), pp. 105–113.
- A.T. Shen, Exponential probability inequalities for WNOD random variables and their applications, RACSAM 110(1) (2016a), pp. 251–268. doi: 10.1007/s13398-015-0233-7
- A.T. Shen, Complete convergence for weighted sums of END random variables and its application to nonparametric regression models, J. Nonparametric Stat. 28 (2016b), pp. 702–715. doi: 10.1080/10485252.2016.1225050
- C.J. Stone, Consistent nonparametric regression, Ann. Stat. 5 (1977), pp. 595–620. doi: 10.1214/aos/1176343886
- W.F. Stout, Almost sure convergence, Academic Press, New York , NY, 1974.
- S.H. Sung, Complete convergence for weighted sums of ρ-mixing random variables, Discrete Dyn. Nature Soc. 2010 (2010), Article ID 630608, 13 pages.
- L. Tran, G. Roussas, S. Yakowitz, and B.T. Van, Fixed-design regression for linear time series, Ann. Stat. 24 (1996), pp. 975–991. doi: 10.1214/aos/1032526952
- X.J. Wang, X. Deng, L.L. Zheng, and S.H. Hu, Complete convergence for arrays of rowwise negatively superadditive dependent random variables and its applications, Stat. J. Theory Appl. Stat. 48(4) (2014a), pp. 834–850.
- X.J. Wang, T.C. Hu, A. Volodin, and S.H. Hu, Complete convergence for weighted sums and arrays of rowwise extended negatively dependent random variables, Commun. Stat. Theory Methods 42 (2013), pp. 2391–2401. doi: 10.1080/03610926.2011.609321
- X.J. Wang and Z.Y. Si, Complete consistency of the estimator of nonparametric regression model under ND sequence, Statist. Papers 56(3) (2015), pp. 585–596. doi: 10.1007/s00362-014-0598-2
- K.Y. Wang, Y.B. Wang, and Q.W. Gao, Uniform asymptotics for the finite-time ruin probability of a new dependent risk model with a constant interest rate, Methodol. Comput. Appl. Probab. 15(1) (2013), pp. 109–124. doi: 10.1007/s11009-011-9226-y
- X.J. Wang, C. Xu, T.C. Hu, A. Volodin, and S.H. Hu, On complete convergence for widely orthant-dependent random variables and its applications in nonparametric regression models, TEST, 23 (2014b), pp. 607–629. doi: 10.1007/s11749-014-0365-7
- X.J. Wang, L.L. Zheng, C. Xu, and S.H. Hu, Complete consistency for the estimator of nonparametric regression models based on extended negatively dependent errors, Stat. J. Theor. Appl. Stat. 49(2) (2015), pp. 396–407.
- C.Q. Wu, M.M. Ning, and A.T. Shen, On complete and complete moment convergence for weighted sums of widely orthant dependent random variables, Filomat 32(15) (2018), pp. 5347–5359. doi: 10.2298/FIL1815347W