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Robust Estimation and Tests for Parameters of Some Nonlinear Regression Models

Author

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  • Pengfei Liu

    (School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China
    Research Institute of Mathematical Sciences, Jiangsu Normal University, Xuzhou 221116, China
    The author order is alphabetically sorted. These authors contributed equally to this work. And the submit author is Ru Zhang.)

  • Mengchen Zhang

    (Department of Public Administration and Policy, College of Public Affairs, National Taipei University, Taipei 237, Taiwan
    The author order is alphabetically sorted. These authors contributed equally to this work. And the submit author is Ru Zhang.)

  • Ru Zhang

    (School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China
    Jiangsu Provincial Key Laboratory of Educational Big Data Science and Engineering, Jiangsu Normal University, Xuzhou 221116, China
    The author order is alphabetically sorted. These authors contributed equally to this work. And the submit author is Ru Zhang.)

  • Qin Zhou

    (School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China
    Research Institute of Mathematical Sciences, Jiangsu Normal University, Xuzhou 221116, China
    The author order is alphabetically sorted. These authors contributed equally to this work. And the submit author is Ru Zhang.)

Abstract

This paper uses the median-of-means (MOM) method to estimate the parameters of the nonlinear regression models and proves the consistency and asymptotic normality of the MOM estimator. Especially when there are outliers, the MOM estimator is more robust than nonlinear least squares (NLS) estimator and empirical likelihood (EL) estimator. On this basis, we propose hypothesis testing Statistics for the parameters of the nonlinear regression models using empirical likelihood method, and the simulation performance shows the superiority of MOM estimator. We apply the MOM method to analyze the top 50 data of GDP of China in 2019. The result shows that MOM method is more feasible than NLS estimator and EL estimator.

Suggested Citation

  • Pengfei Liu & Mengchen Zhang & Ru Zhang & Qin Zhou, 2021. "Robust Estimation and Tests for Parameters of Some Nonlinear Regression Models," Mathematics, MDPI, vol. 9(6), pages 1-16, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:6:p:599-:d:514869
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    References listed on IDEAS

    as
    1. Guillaume Lecué & Mathieu Lerasle, 2017. "Robust machine learning by median-of-means : theory and practice," Working Papers 2017-32, Center for Research in Economics and Statistics.
    2. Pollard, David & Radchenko, Peter, 2006. "Nonlinear least-squares estimation," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 548-562, February.
    3. Yin, Cangtao & Du, Jiulin, 2014. "The collision theory reaction rate coefficient for power-law distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 119-127.
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