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

Hongchang Hu, Mingqiu Liu and Zhen Zeng ()
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Hongchang Hu: Hubei Normal University
Mingqiu Liu: Hubei Normal University
Zhen Zeng: Nanjing University of Finance and Economics

Metrika: International Journal for Theoretical and Applied Statistics, 2025, vol. 88, issue 1, No 1, 18 pages

Abstract: 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.

Keywords: Generalized linear models; Penalized Lq-likelihood estimator; Oracle property; Influence function; 62J12; 62J07; 62F12 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00184-023-00943-z

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