论文标题
通过logit变换的稳健beta回归
Robust beta regression through the logit transformation
论文作者
论文摘要
Beta回归模型用于在单位间隔(例如速率,百分比或比例)中对连续响应变量进行建模。它们在医学,环境研究,金融和自然科学等多个领域的应用。最大似然估计广泛用于推断参数。尽管如此,众所周知,基于最大似然的推理在异常值的存在下缺乏鲁棒性。这样的案例会带来严重的偏见和误导性结论。最近,文献中介绍了Beta回归模型的强大估计器。但是,这些估计器需要在参数空间中进行非平凡的限制,这限制了其应用程序。本文开发了新的稳健估计器,以克服这一缺点。研究了它们的渐近性和鲁棒性特性,并引入了稳健的WALD型测试。仿真结果证明了新的稳健估计器的优点。使用新估计量的推论和诊断在健康保险范围数据的应用中说明了。
Beta regression models are employed to model continuous response variables in the unit interval, like rates, percentages, or proportions. Their applications rise in several areas, such as medicine, environment research, finance, and natural sciences. The maximum likelihood estimation is widely used to make inferences for the parameters. Nonetheless, it is well-known that the maximum likelihood-based inference suffers from the lack of robustness in the presence of outliers. Such a case can bring severe bias and misleading conclusions. Recently, robust estimators for beta regression models were presented in the literature. However, these estimators require non-trivial restrictions in the parameter space, which limit their application. This paper develops new robust estimators that overcome this drawback. Their asymptotic and robustness properties are studied, and robust Wald-type tests are introduced. Simulation results evidence the merits of the new robust estimators. Inference and diagnostics using the new estimators are illustrated in an application to health insurance coverage data.