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On Complete Consistency for the Estimator of Nonparametric Regression Model Based on Asymptotically Almost Negatively Associated Errors

Author

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  • Aiting Shen

    (Anhui University)

  • Siyao Zhang

    (Anhui University)

Abstract

In this paper, we mainly study the consistency for the estimator of nonparametric regression model based on asymptotically almost negatively associated (AANA, in short) errors. Firstly, the Bernstein type inequality for AANA random variables is established. By using the Bernstein type inequality and moment inequalities, we investigate the complete consistency and convergence rate for the estimator of nonparametric regression model based on AANA errors. As applications, the complete consistency and convergence rate for the nearest neighbor estimator are obtained.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:23:y:2021:i:4:d:10.1007_s11009-020-09813-x
    DOI: 10.1007/s11009-020-09813-x
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    References listed on IDEAS

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    1. Xuejun Wang & Zeyu Si, 2015. "Complete consistency of the estimator of nonparametric regression model under ND sequence," Statistical Papers, Springer, vol. 56(3), pages 585-596, August.
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    5. Aiting Shen, 2013. "Bernstein-Type Inequality for Widely Dependent Sequence and Its Application to Nonparametric Regression Models," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, July.
    6. Roussas, George G., 1989. "Consistent regression estimation with fixed design points under dependence conditions," Statistics & Probability Letters, Elsevier, vol. 8(1), pages 41-50, May.
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    8. 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.
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