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Large deviation inequalities of Bayesian estimator in nonlinear regression models

Author

Listed:
  • Yu Miao

    (Henan Normal University
    Henan Normal University)

  • Yanyan Tang

    (Henan Normal University)

Abstract

In the present paper, we establish some large deviation inequalities of the Bayesian estimator for the nonlinear regression model under the conditions of dependent errors which extend the results in Jeganathan (J Multivar Anal 30(2):227–240, 1989) from independent errors and dependent sequences. As an application, we give an large deviation inequality for the Michaelis–Menten model.

Suggested Citation

  • Yu Miao & Yanyan Tang, 2023. "Large deviation inequalities of Bayesian estimator in nonlinear regression models," Statistical Inference for Stochastic Processes, Springer, vol. 26(1), pages 171-191, April.
    • Handle: RePEc:spr:sistpr:v:26:y:2023:i:1:d:10.1007_s11203-022-09280-w
    DOI: 10.1007/s11203-022-09280-w
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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. Jeganathan, P., 1989. "A note on inequalities for probabilities of large deviations of estimators in nonlinear regression models," Journal of Multivariate Analysis, Elsevier, vol. 30(2), pages 227-240, August.
    3. Qi-Man Shao, 2000. "A Comparison Theorem on Moment Inequalities Between Negatively Associated and Independent Random Variables," Journal of Theoretical Probability, Springer, vol. 13(2), pages 343-356, April.
    Full references (including those not matched with items on IDEAS)

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