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The large deviation results for the nonlinear regression model with dependent errors

Author

Listed:
  • Wenzhi Yang

    (Anhui University)

  • Zhangrui Zhao

    (Anhui University)

  • Xinghui Wang

    (Anhui University)

  • Shuhe Hu

    (Anhui University)

Abstract

In this paper, we investigate the least squares (LS) estimator of the nonlinear regression model based on the extended negatively dependent errors which are widely dependent structures. Under the general conditions, we establish some large deviation results for the LS estimator of the nonlinear regression parameter, which can be applied to obtain a weak uniform consistency and a complete convergence rate for this estimator. In addition, some examples and simulations are presented for illustration.

Suggested Citation

  • Wenzhi Yang & Zhangrui Zhao & Xinghui Wang & Shuhe Hu, 2017. "The large deviation results for the nonlinear regression model with dependent errors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(2), pages 261-283, June.
    • Handle: RePEc:spr:testjl:v:26:y:2017:i:2:d:10.1007_s11749-016-0509-z
    DOI: 10.1007/s11749-016-0509-z
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    References listed on IDEAS

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    1. Yang, Wenzhi & Hu, Shuhe, 2014. "Large deviation for a least squares estimator in a nonlinear regression model," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 135-144.
    2. Habshah Midi, 1999. "Preliminary estimators for robust non-linear regression estimation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(5), pages 591-600.
    3. Liu, Li, 2009. "Precise large deviations for dependent random variables with heavy tails," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1290-1298, May.
    4. 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.
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    Cited by:

    1. Hongyan Fang & Saisai Ding & Xiaoqin Li & Wenzhi Yang, 2020. "Asymptotic Approximations of Ratio Moments Based on Dependent Sequences," Mathematics, MDPI, vol. 8(3), pages 1-18, March.

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