Complete consistency for the estimator of nonparametric regression model based on martingale difference errors

References

• Chen, X., and H. J. Cui. 2008. Empirical likelihood inference for partial linear models under martingale difference sequence. Statistics Probability Letters 78 (17):2895–901. doi:10.1016/j.spl.2008.04.012.
   Web of Science ®Google Scholar
• Chen, Z. Y., H. B. Wang, and X. J. Wang. 2016. The consistency for the estimator of nonparametric regression model based on martingale difference errors. Statistical Papers 57 (2):451–69. doi:10.1007/s00362-015-0662-6.
   Web of Science ®Google Scholar
• Fan, Y. 1990. Consistent nonparametric multiple regression for dependent heterogeneous processes: The fixed design case. Journal of Multivariate Analysis 33 (1):72–88. doi:10.1016/0047-259X(90)90006-4.
   Web of Science ®Google Scholar
• Fan, G. L., and H. Y. Liang. 2010. Empirical likelihood inference for semiparametric model with linear process errors. Journal of the Korean Statistical Society 39 (1):55–65. doi:10.1016/j.jkss.2009.04.001.
   Web of Science ®Google Scholar
• Gasser, T., and H. G. Müller. 1979. Kernel estimation of regression functions. Smoothing techniques for curve estimation. Berlin, Germany: Springer.
   Google Scholar
• Georgiev, A. A., and W. Greblicki. 1986. Nonparametric function recovering from noisy observations. Journal of Statistical Planning and Inference 13 (1):1–14. doi:10.1016/0378-3758(86)90114-X.
   Web of Science ®Google Scholar
• Hsu, P. L., and H. Robbins. 1947. Complete convergence and the law of large numbers. Proceedings of the National Academy of Sciences of the United States of America 33 (2):25–31. doi:10.1073/pnas.33.2.25.
   PubMed Web of Science ®Google Scholar
• Kuczmaszewska, A. 2010. On complete convergence in Marcinkiewicz-Zygmund type SLLN for negatively associated random variables. Acta Mathematica Hungarica 128 (1–2):116–30. doi:10.1007/s10474-009-9166-y.
   Web of Science ®Google Scholar
• Laib, N. 1999. Exponential-type inequalities for martingale difference sequences. Application to nonparametric regression estimation. Communication in Statistics - Theory and Methods 28 (7):1565–76. doi:10.1080/03610929908832373.
   Web of Science ®Google Scholar
• Li, Y. L. 2003. A martingale inequality and large deviations. Statistics Probability Letters 62 (3):317–21. doi:10.1016/S0167-7152(03)00046-4.
   Web of Science ®Google Scholar
• Liang, H. Y., and B. Y. Jing. 2005. Asymptotic properties for estimates of nonparametric regression models based on negatively associated sequences. Journal of Multivariate Analysis 95 (2):227–45. doi:10.1016/j.jmva.2004.06.004.
   Web of Science ®Google Scholar
• Miao, Y., Y. L. Wang, and H. J. Zheng. 2015. Consistency of LS estimators in EV regression model with martingale difference errors. Statistics 49 (1):104–18. doi:10.1080/02331888.2014.903950.
   Web of Science ®Google Scholar
• Müller, H. G. 1987. Weak and universal consistency of moving weighted averages. Periodica Mathematica Hungarica 18 (3):241–50. doi:10.1007/BF01848087.
   Google Scholar
• Priestley, M. B., and M. T. Chao. 1972. Non-parametric function fitting. Journal of the Royal Statistical Society 34 (3):385–92. doi:10.1111/j.2517-6161.1972.tb00916.x.
   Google Scholar
• Shen, A. T., M. M. Ning, and C. Q. Wu. 2019. The asymptotic normality of the linear weighted estimator in nonparametric regression models. Communication in Statistics - Theory and Methods 48 (6):1367–76. doi:10.1080/03610926.2018.1429633.
   Web of Science ®Google Scholar
• Tran, L., G. Roussas, S. Yakowitz, and B. Truong Van. 1996. Fixed-design regression for linear time series. The Annals of Statistics 24 (3):975–91. doi:10.1214/aos/1032526952.
   Web of Science ®Google Scholar
• Wang, X. J., Y. Wu, and S. H. Hu. 2018a. The Berry–Esseen bounds of the weighted estimator in a nonparametric regression model. Annals of the Institute of Statistical Mathematics. doi:10.1007/s10463-018-0677-6.
   PubMed Web of Science ®Google Scholar
• Wang, X. J., Y. Wu, S. H. Hu, and N. X. Ling. 2018b. Complete moment convergence for negatively orthant dependent random variables and its applications in statistical models. Statistical Papers. doi:10.1007/s00362-018-0983-3.
   Web of Science ®Google Scholar
• Yang, W. Z., X. J. Wang, X. G. Wang, and S. H. Hu. 2012. The consistency for estimator of nonparametric regression model based on NOD errors. Journal of Inequalities and Applications 2012 (1):140–13. doi:10.1186/1029-242X-2012-140.
   Web of Science ®Google Scholar
• Yang, W. Z., H. Y. Xu, L. Chen, and S. H. Hu. 2016. Complete consistency of estimators for regression model based on extended negatively dependent errors. Statistical Papers 59 (2):449–65. doi:10.1007/s00362-016-0771-x.
   Web of Science ®Google Scholar
• Zhao, Z. W., D. H. Wang, and Y. Zhang. 2011. Limit theory for random coefficient first-order autoregressive process under martingale difference error sequence. Journal of Computational and Applied Mathematics 235 (8):2515–22. doi:10.1016/j.cam.2010.11.004.
   Web of Science ®Google Scholar