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Penalized Lq-likelihood estimator and its influence function in generalized linear models

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  • Hongchang Hu

    (Hubei Normal University)

  • Mingqiu Liu

    (Hubei Normal University)

  • Zhen Zeng

    (Nanjing University of Finance and Economics)

Abstract

Consider the following generalized linear model (GLM) $$\begin{aligned} y_i=h(x_i^T\beta )+e_i,\quad i=1,2,\ldots ,n, \end{aligned}$$ y i = h ( x i T β ) + e i , i = 1 , 2 , … , n , where h(.) is a continuous differentiable function, $$\{e_i\}$$ { e i } are independent identically distributed (i.i.d.) random variables with zero mean and known variance $$\sigma ^2$$ σ 2 . Based on the penalized Lq-likelihood method of linear regression models, we apply the method to the GLM, and also investigate Oracle properties of the penalized Lq-likelihood estimator (PLqE). In order to show the robustness of the PLqE, we discuss influence function of the PLqE. Simulation results support the validity of our approach. Furthermore, it is shown that the PLqE is robust, while the penalized maximum likelihood estimator is not.

Suggested Citation

  • Hongchang Hu & Mingqiu Liu & Zhen Zeng, 2025. "Penalized Lq-likelihood estimator and its influence function in generalized linear models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 88(1), pages 1-18, January.
    • Handle: RePEc:spr:metrik:v:88:y:2025:i:1:d:10.1007_s00184-023-00943-z
    DOI: 10.1007/s00184-023-00943-z
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    References listed on IDEAS

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