基于概率积分变换的正态分位数的广义线性模型稳健估计

中文摘要 AI 辅助

本文提出了一种广义线性模型稳健估计的新方法，该方法的核心思路是先对响应变量应用正态分位数函数与概率积分变换的复合变换，再利用变换后响应变量应服从标准正态分布的特性，寻找能最小化其大小的稳健度量的参数值，实际应用中使用该变换的近似形式。本文对依赖单一参数的分布从理论上研究了所提估计量，并通过模拟和实例针对泊松回归与逻辑回归这两种特定情形进行了分析。

英文摘要

A new approach to robust estimation in generalized linear models is introduced. The idea of the method is to first transform the responses applying the composition of the normal quantile function and the probability integral transformation. Then, using that the transformed responses should follow a standard normal distribution, find the values of the parameters that minimize a robust measure of their size. In practice an approximation of this transformation is used. The proposed estimators are studied theoretically for distributions that depend on a single parameter and through simulations and examples for the particular cases of Poisson and logistic regression.

发表机构

• Instituto de Cálculo, University of Buenos Aires（计算研究所，布宜诺斯艾利斯大学）
• CONICET（阿根廷国家科学研究委员会）
• Instituto de Cálculo and Department of Mathematics, FCEN, University of Buenos Aires（计算研究所与数学系，理学院，布宜诺斯艾利斯大学）

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