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On the M-Estimator under Third Moment Condition

Author

Listed:
  • Rundong Luo

    (School of Business, Shandong University, Weihai 264209, China)

  • Yiming Chen

    (Institute for Financial Studies, Shandong University, Jinan 250100, China)

  • Shuai Song

    (School of Economics, Shandong University, Jinan 250100, China)

Abstract

Estimating the expected value of a random variable by data-driven methods is one of the most fundamental problems in statistics. In this study, we present an extension of Olivier Catoni’s classical M-estimators of the empirical mean, which focus on the heavy-tailed data by imposing more precise inequalities on exponential moments of Catoni’s estimator. We show that our works behave better than Catoni‘s both in practice and theory. The performances are illustrated in the simulation and real data.

Suggested Citation

  • Rundong Luo & Yiming Chen & Shuai Song, 2022. "On the M-Estimator under Third Moment Condition," Mathematics, MDPI, vol. 10(10), pages 1-16, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1713-:d:817490
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    References listed on IDEAS

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    1. Christian E. Galarza & Panpan Zhang & Víctor H. Lachos, 2021. "Logistic Quantile Regression for Bounded Outcomes Using a Family of Heavy-Tailed Distributions," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 325-349, November.
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