194
Views
31
CrossRef citations to date
0
Altmetric
Original Articles

Complete convergence for weighted sums of END random variables and its application to nonparametric regression models

Pages 702-715 | Received 09 Sep 2015, Accepted 31 May 2016, Published online: 30 Aug 2016

References

  • Baum, L.E., and Katz, M. (1965), ‘Convergence Rates in the Law of Large Numbers’, Transactions of the American Mathematical Society, 120, 108–123. doi: 10.1090/S0002-9947-1965-0198524-1
  • Chen, P.Y., Bai, P., and Sung, S.H. (2014), ‘The von Bahr-Esseen Moment Inequality for Pairwise Independent Random Variables and Applications’, Journal of Mathematical Analysis and Applications, 419, 1290–1302. doi: 10.1016/j.jmaa.2014.05.067
  • Chen, Y., Chen, A., and Ng, K.W. (2010), ‘The Strong Law of Large Numbers for Extended Negatively Dependent Random Variables’, Journal of Applied Probability, 47, 908–922. doi: 10.1017/S0021900200007257
  • Erdös, P. (1949), ‘On a Theorem of Hsu and Robbins’, The Annals of Mathematical Statistics, 20, 286–291. doi: 10.1214/aoms/1177730037
  • Fan, Y. (1990), ‘Consistent Nonparametric Multiple Regression for Dependent Heterogeneous Processes: The Fixed Design Case’, Journal of Multivariate Analysis, 33, 72–88. doi: 10.1016/0047-259X(90)90006-4
  • Georgiev, A.A. (1985), ‘Local Properties of Function Fitting Estimates with Applications to System Identification’, in Mathematical Statistics and Applications, eds. W. Grossmann et al., Proceedings 4th Pannonian Sump. Math. Statist., 4–10 September 1983, Bad Tatzmannsdorf, Austria: Reidel, Dordrecht, pp. 141–151.
  • Georgiev, A.A. (1988), ‘Consistent Nonparametric Multiple Regression: The Fixed Design Case’, Journal of Multivariate Analysis, 25, 100–110. doi: 10.1016/0047-259X(88)90155-8
  • Georgiev, A.A., and Greblicki, W. (1986), ‘Nonparametric Function Recovering from Noisy Observations’, Journal of Statistical Planning and Inference, 13, 1–14. doi: 10.1016/0378-3758(86)90114-X
  • Hsu, P. L., and Robbins, H. (1947), ‘Complete Convergence and the Law of Large Numbers’, Proceedings of the National Academy of Sciences, 33, 25–31. doi: 10.1073/pnas.33.2.25
  • Hu, S.H., Zhu, C.H., Chen, Y.B., and Wang, L.C. (2002), ‘Fixed-design Regression for Linear Time Series’, Acta Mathematica Scientia, 22B, 9–18.
  • Hu, T.C., Wang, K.L., and Rosalsky, A. (2015), ‘Complete Convergence Theorems for Extended Negatively Dependent Random Variables’, Sankhya A, 77, 1–29. doi: 10.1007/s13171-014-0058-z
  • Joag-Dev, K., and Proschan, F. (1983), ‘Negative Association of Random Variables with Applications’, The Annals of Statistics, 11, 286–295. doi: 10.1214/aos/1176346079
  • Liang, H.Y., and Jing, B.Y. (2005), ‘Asymptotic Properties for Estimates of Nonparametric Regression Models based on Negatively Associated Sequences’, Journal of Multivariate Analysis, 95, 227–245. doi: 10.1016/j.jmva.2004.06.004
  • Liu, L. (2009), ‘Precise Large Deviations for Dependent Random Variables with Heavy Tails’, Statistics & Probability Letters, 79, 1290–1298. doi: 10.1016/j.spl.2009.02.001
  • Müller, H.G. (1987), ‘Weak and Universal Consistency of Moving Weighted Averages’, Periodica Mathematica Hungarica, 18, 241–250. doi: 10.1007/BF01848087
  • Qiu, D.H., Chen, P.Y., Antonini, R.G., and Volodin, A. (2013), ‘On the Complete Convergence for Arrays of Rowwise Extended Negatively Dependent Random Variables’, Journal of the Korean Mathematical Society, 50, 379–392. doi: 10.4134/JKMS.2013.50.2.379
  • Roussas, G.G. (1989), ‘Consistent Regression Estimation with Fixed Design Points under Dependence Conditions’, Statistics & Probability Letters, 8, 41–50. doi: 10.1016/0167-7152(89)90081-3
  • Roussas, G.G., Tran, L.T., and Ioannides, D.A. (1992), ‘Fixed Design Regression for Time Series: Asymptotic Normality’, Journal of Multivariate Analysis, 40, 262–291. doi: 10.1016/0047-259X(92)90026-C
  • Shen, A. (2011), ‘Probability inequalities for END sequence and their applications’, Journal of Inequalities and Applications, 2011, 12 pages, Article ID 98.
  • Stone, C.J. (1977), ‘Consistent Nonparametric Regression’, The Annals of Statistics, 5, 595–620. doi: 10.1214/aos/1176343886
  • Tran, L. Roussas, G. Yakowitz, S., and Van, B.T. (1996), ‘Fixed-design Regression for Linear Time Series’, The Annals of Statistics, 24, 975–991. doi: 10.1214/aos/1032526952
  • Wang, S.J., and Wang, X.J. (2013), ‘Precise Large Deviations for Random Sums of END Real-valued Random Variables with Consistent Variation’, Journal of Mathematical Analysis and Applications, 402, 660–667. doi: 10.1016/j.jmaa.2013.02.002
  • Wang, X.J., Hu, T.C., Volodin, A., and Hu, S.H. (2013a), ‘Complete Convergence for Weighted Sums and Arrays of Rowwise Extended Negatively Dependent Random Variables’, Communications in Statistics – Theory and Methods, 42, 2391–2401. doi: 10.1080/03610926.2011.609321
  • Wang, X.J., Wang, S.J., Hu, S.H., Ling, J.M., and Wei, Y.F. (2013b), ‘On Complete Convergence of Weighted Sums for Arrays of Rowwise Extended Negatively Dependent Random Variables’, Stochastics: An International Journal of Probability and Stochastic Processes, 85, 1060–1072.
  • Wang, X.J., Deng, X., Zheng, L.L., and Hu, S.H. (2014a), ‘Complete Convergence for Arrays of Rowwise Negatively Superadditive-dependent Random Variables and its Applications’, Statistics: A Journal of Theoretical and Applied Statistics, 48, 834–850. doi: 10.1080/02331888.2013.800066
  • Wang, X.J., Li, X.Q., Hu, S.H., and Wang, X.H. (2014b), ‘On Complete Convergence for an Extended Negatively Dependent Sequence’, Communications in Statistics – Theory and Methods, 43, 2923–2937. doi: 10.1080/03610926.2012.690489
  • Wang, X.J., Xu, C., Hu, T.-C., Volodin, A., and Hu, S.H. (2014c), ‘On Complete Convergence for Widely Orthant-dependent Random Variables and its Applications in Nonparametric Regression Models’, TEST, 23, 607–629. doi: 10.1007/s11749-014-0365-7
  • Wang, X.J., Zheng, L.L., Xu, C., and Hu, S.H. (2015), ‘Complete Consistency for the Estimator of Nonparametric Regression Models based on Extended Negatively Dependent Errors’, Statistics: A Journal of Theoretical and Applied Statistics, 49, 396–407. doi: 10.1080/02331888.2014.888431
  • Wu, Y.F., and Guan, M. (2012), ‘Convergence Properties of the Partial Sums for Sequences of END Random Variables’, Journal of the Korean Mathematical Society, 49, 1097–1110. doi: 10.4134/JKMS.2012.49.6.1097
  • Yang, W.Z., Wang, X.J., Wang, X.H., and Hu, S.H. (2012), ‘The Consistency for Estimator of Nonparametric Regression Model Based on NOD Errors’, Journal of Inequalities and Applications, 2012, 13 pages, Article ID 140.

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.