Yuri S. Maluf, Silvia L. P. Ferrari, Francisco F. Queiroz
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引用次数: 0
摘要
贝塔回归模型用于对单位区间内的连续响应变量(如比率、百分比或比例)进行建模。贝塔回归模型在医学、环境研究、金融和自然科学等多个领域得到广泛应用。最大似然估计法被广泛用于推断参数。然而,众所周知,基于最大似然法的推断在出现异常值时缺乏稳健性。这种情况会带来严重的偏差和误导性结论。最近,文献中出现了贝塔回归模型的稳健估计器。然而,这些估计器需要对参数空间进行非难度限制,这限制了它们的应用。本文开发了新的稳健估计器,克服了这一缺点。本文研究了它们的渐近性和稳健性,并引入了稳健的沃尔德类型检验。模拟结果证明了新稳健估计器的优点。在医疗保险覆盖数据的应用中,对使用新估计器进行推断和诊断进行了说明。介绍了新的 R 软件包 robustbetareg。
Robust beta regression through the logit transformation
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. The new R package robustbetareg is introduced.
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.