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

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Metrika Pub Date : 2024-01-07 DOI:10.1007/s00184-023-00943-z

引用次数: 0

Abstract

Consider the following generalized linear model (GLM) $$\begin{aligned} y_i=h(x_i^T\beta )+e_i,\quad i=1,2,\ldots ,n, \end{aligned}$$ where h(.) is a continuous differentiable function, $\{e_i\}$ are independent identically distributed (i.i.d.) random variables with zero mean and known variance $\sigma ^2$ . 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.

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广义线性模型中的惩罚性 Lq-似然估计器及其影响函数

Abstract Consider the following generalized linear model (GLM) $$begin{aligned} y_i=h(x_i^T\beta )+e_i,\quad i=1,2,\ldots ,n, \end{aligned}$$其中h(.)是连续可微分函数，(\{e_i\}\)是均值为零且方差为已知的独立同分布（i.i.d.）随机变量。基于线性回归模型的惩罚性 Lq-likelihood 方法，我们将该方法应用于 GLM，并研究了惩罚性 Lq-likelihood 估计器（PLqE）的 Oracle 特性。为了证明 PLqE 的稳健性，我们讨论了 PLqE 的影响函数。模拟结果证明了我们方法的有效性。此外，仿真结果表明 PLqE 是稳健的，而惩罚最大似然估计器则不稳健。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Metrika 数学-统计学与概率论

CiteScore

1.50

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： Metrika is an international journal for theoretical and applied statistics. Metrika publishes original research papers in the field of mathematical statistics and statistical methods. Great importance is attached to new developments in theoretical statistics, statistical modeling and to actual innovative applicability of the proposed statistical methods and results. Topics of interest include, without being limited to, multivariate analysis, high dimensional statistics and nonparametric statistics; categorical data analysis and latent variable models; reliability, lifetime data analysis and statistics in engineering sciences.