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Complete Consistency of the Estimator of Nonparametric Regression Models Based on -Mixing Sequences

Author

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  • Xuejun Wang
  • Fengxi Xia
  • Meimei Ge
  • Shuhe Hu
  • Wenzhi Yang

Abstract

We study the complete consistency for estimator of nonparametric regression model based on -mixing sequences by using the classical Rosenthal-type inequality and the truncated method. As an application, the complete consistency for the nearest neighbor estimator is obtained.

Suggested Citation

  • Xuejun Wang & Fengxi Xia & Meimei Ge & Shuhe Hu & Wenzhi Yang, 2012. "Complete Consistency of the Estimator of Nonparametric Regression Models Based on -Mixing Sequences," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-12, December.
    • Handle: RePEc:hin:jnlaaa:907286
    DOI: 10.1155/2012/907286
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    Cited by:

    1. Aiting Shen & Siyao Zhang, 2021. "On Complete Consistency for the Estimator of Nonparametric Regression Model Based on Asymptotically Almost Negatively Associated Errors," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1285-1307, December.
    2. Liwang Ding & Ping Chen & Yongming Li, 2020. "Consistency for wavelet estimator in nonparametric regression model with extended negatively dependent samples," Statistical Papers, Springer, vol. 61(6), pages 2331-2349, December.
    3. Xuejun Wang & Yi Wu & Shuhe Hu & Nengxiang Ling, 2020. "Complete moment convergence for negatively orthant dependent random variables and its applications in statistical models," Statistical Papers, Springer, vol. 61(3), pages 1147-1180, June.
    4. Xuejun Wang & Yi Wu & Shuhe Hu, 2019. "The Berry–Esseen bounds of the weighted estimator in a nonparametric regression model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1143-1162, October.
    5. Yan, Ji Gao, 2018. "On Complete Convergence in Marcinkiewicz-Zygmund Type SLLN for END Random Variables and its Applications," IRTG 1792 Discussion Papers 2018-042, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".

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