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1. A. A. Georgiev, “Local properties of function fitting estimates with application to system identification,” in Proceedings of the 4th Pannonian Symposium on Mathematical Statistics, W. Grossmann, Ed., Mathematical Statistics and Applications, pp. 141–151, Bad Tatzmannsdorf, Dordrecht, The Netherlands, 1983.
2. A. A. Georgiev and W. Greblicki, “Nonparametric function recovering from noisy observations,” Journal of Statistical Planning and Inference, vol. 13, no. 1, pp. 1–14, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
3. A. A. Georgiev, “Consistent nonparametric multiple regression: the fixed design case,” Journal of Multivariate Analysis, vol. 25, no. 1, pp. 100–110, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
4. H.-G. Müller, “Weak and universal consistency of moving weighted averages,” Periodica Mathematica Hungarica, vol. 18, no. 3, pp. 241–250, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
5. Y. Fan, “Consistent nonparametric multiple regression for dependent heterogeneous processes: the fixed design case,” Journal of Multivariate Analysis, vol. 33, no. 1, pp. 72–88, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
6. G. G. Roussas, “Consistent regression estimation with fixed design points under dependence conditions,” Statistics & Probability Letters, vol. 8, no. 1, pp. 41–50, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
7. G. G. Roussas, L. T. Tran, and D. A. Ioannides, “Fixed design regression for time series: asymptotic normality,” Journal of Multivariate Analysis, vol. 40, no. 2, pp. 262–291, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
8. L. Tran, G. Roussas, S. Yakowitz, and B. Truong Van, “Fixed-design regression for linear time series,” The Annals of Statistics, vol. 24, no. 3, pp. 975–991, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
9. S. H. Hu, C. H. Zhu, Y. B. Chen, and L. C. Wang, “Fixed-design regression for linear time series,” Acta Mathematica Scientia, vol. 22, no. 1, pp. 9–18, 2002. View at Zentralblatt MATH
10. S. H. Hu, G. M. Pan, and Q. B. Gao, “Estimation problems for a regression model with linear process errors,” Applied Mathematics, vol. 18, no. 1, pp. 81–90, 2003.
11. H.-Y. Liang and B.-Y. Jing, “Asymptotic properties for estimates of nonparametric regression models based on negatively associated sequences,” Journal of Multivariate Analysis, vol. 95, no. 2, pp. 227–245, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
12. W. Z. Yang, X. J. Wang, X. H. Wang, and S. H. Hu, “The consistency for estimator of nonparametricregression model based on NOD errors,” Journal of Inequalities and Applications, vol. 2012, 140, 2012.
13. R. C. Bradley, “On the spectral density and asymptotic normality of weakly dependent random fields,” Journal of Theoretical Probability, vol. 5, no. 2, pp. 355–373, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
14. W. Bryc and W. Smoleński, “Moment conditions for almost sure convergence of weakly correlated random variables,” Proceedings of the American Mathematical Society, vol. 119, no. 2, pp. 629–635, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
15. M. Peligrad, “Maximum of partial sums and an invariance principle for a class of weak dependent random variables,” Proceedings of the American Mathematical Society, vol. 126, no. 4, pp. 1181–1189, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
16. S. Utev and M. Peligrad, “Maximal inequalities and an invariance principle for a class of weakly dependent random variables,” Journal of Theoretical Probability, vol. 16, no. 1, pp. 101–115, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
17. S. X. Gan, “Almost sure convergence for $\tilde{\rho }$-mixing random variable sequences,” Statistics & Probability Letters, vol. 67, no. 4, pp. 289–298, 2004. View at Publisher · View at Google Scholar
18. A. Kuczmaszewska, “On Chung-Teicher type strong law of large numbers for ${\rho }^{*}$-mixing random variables,” Discrete Dynamics in Nature and Society, vol. 2008, Article ID 140548, 10 pages, 2008. View at Publisher · View at Google Scholar
19. Q. Y. Wu and Y. Y. Jiang, “Some strong limit theorems for $\tilde{\rho }$-mixing sequences of random variables,” Statistics & Probability Letters, vol. 78, no. 8, pp. 1017–1023, 2008. View at Publisher · View at Google Scholar
20. X. J. Wang, S. H. Hu, Y. Shen, and N. X. Ling, “Strong law of large numbers and growth rate for a class of random variable sequence,” Statistics & Probability Letters, vol. 78, no. 18, pp. 3330–3337, 2008. View at Publisher · View at Google Scholar
21. M. Peligrad and A. Gut, “Almost-sure results for a class of dependent random variables,” Journal of Theoretical Probability, vol. 12, no. 1, pp. 87–104, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
22. G.-H. Cai, “Strong law of large numbers for $\tilde{\rho }$-mixing sequences with different distributions,” Discrete Dynamics in Nature and Society, vol. 2006, Article ID 27648, 7 pages, 2006. View at Publisher · View at Google Scholar
23. A. Kuczmaszewska, “On complete convergence for arrays of rowwise dependent random variables,” Statistics & Probability Letters, vol. 77, no. 11, pp. 1050–1060, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
24. M.-H. Zhu, “Strong laws of large numbers for arrays of rowwise $\tilde{\rho }$-mixing random variables,” Discrete Dynamics in Nature and Society, vol. 2007, Article ID 74296, 6 pages, 2007. View at Publisher · View at Google Scholar
25. J. An and D. M. Yuan, “Complete convergence of weighted sums for ${\rho }^{*}$-mixing sequence of random variables,” Statistics & Probability Letters, vol. 78, no. 12, pp. 1466–1472, 2008. View at Publisher · View at Google Scholar
26. S. H. Sung, “Complete convergence for weighted sums of $\tilde{\rho }$-mixing random variables,” Discrete Dynamics in Nature and Society, vol. 2010, Article ID 630608, 13 pages, 2010. View at Publisher · View at Google Scholar
27. X. J. Wang, X. Q. Li, W. Z. Yang, and S. H. Hu, “On complete convergence for arrays of rowwiseweakly dependent random variables,” Applied Mathematics Letters, vol. 25, no. 11, pp. 1916–1920, 2012. View at Publisher · View at Google Scholar
28. X. C. Zhou, C. C. Tan, and J. G. Lin, “On the strong laws for weighted sums of ${\rho }^{*}$-mixing random variables,” Journal of Inequalities and Applications, vol. 2011, Article ID 157816, 8 pages, 2011. View at Publisher · View at Google Scholar
29. S. H. Sung, “On the strong convergence for weighted sums of ${\rho }^{*}$-mixing random variables,” Statistical Papers. In press. View at Publisher · View at Google Scholar