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Complete consistency of the estimator of nonparametric regression model under ND sequence

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  • Xuejun Wang
  • Zeyu Si

Abstract

In this paper, we study the complete consistency of estimator of nonparametric regression model based on negatively dependent errors by using the classical Rosenthal-type inequality and the truncated method. As an application, the complete consistency for the nearest neighbor estimator is obtained. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:56:y:2015:i:3:p:585-596
    DOI: 10.1007/s00362-014-0598-2
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    References listed on IDEAS

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    1. Wang, Xuejun & Hu, Shuhe & Yang, Wenzhi & Ling, Nengxiang, 2010. "Exponential inequalities and inverse moment for NOD sequence," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 452-461, March.
    2. Fan, Y., 1990. "Consistent nonparametric multiple regression for dependent heterogeneous processes: The fixed design case," Journal of Multivariate Analysis, Elsevier, vol. 33(1), pages 72-88, April.
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    6. Liang, Han-Ying & Jing, Bing-Yi, 2005. "Asymptotic properties for estimates of nonparametric regression models based on negatively associated sequences," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 227-245, August.
    7. Roussas, George G. & Tran, Lanh T. & Ioannides, D. A., 1992. "Fixed design regression for time series: Asymptotic normality," Journal of Multivariate Analysis, Elsevier, vol. 40(2), pages 262-291, February.
    8. Georgiev, Alexander A., 1988. "Consistent nonparametric multiple regression: The fixed design case," Journal of Multivariate Analysis, Elsevier, vol. 25(1), pages 100-110, April.
    9. Klesov, Oleg & Rosalsky, Andrew & Volodin, Andrei I., 2005. "On the almost sure growth rate of sums of lower negatively dependent nonnegative random variables," Statistics & Probability Letters, Elsevier, vol. 71(2), pages 193-202, February.
    10. Amini, M. & Zarei, H. & Bozorgnia, A., 2007. "Some strong limit theorems of weighted sums for negatively dependent generalized Gaussian random variables," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1106-1110, June.
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    Citations

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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. Xin Deng & Xuejun Wang, 2020. "An exponential inequality and its application to M estimators in multiple linear models," Statistical Papers, Springer, vol. 61(4), pages 1607-1627, August.
    3. 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.
    4. Xin Deng & Xuejun Wang & Yi Wu, 2021. "The Berry–Esseen type bounds of the weighted estimator in a nonparametric model with linear process errors," Statistical Papers, Springer, vol. 62(2), pages 963-984, April.
    5. Aiting Shen & Andrei Volodin, 2017. "Weak and strong laws of large numbers for arrays of rowwise END random variables and their applications," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(6), pages 605-625, November.
    6. Mengmei Xi & Rui Wang & Zhaoyang Cheng & Xuejun Wang, 2020. "Some convergence properties for partial sums of widely orthant dependent random variables and their statistical applications," Statistical Papers, Springer, vol. 61(4), pages 1663-1684, August.
    7. Wenzhi Yang & Haiyun Xu & Ling Chen & Shuhe Hu, 2018. "Complete consistency of estimators for regression models based on extended negatively dependent errors," Statistical Papers, Springer, vol. 59(2), pages 449-465, June.

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