Jaenada María, Miranda Pedro, Pardo Leandro
Department of Statistics and Operation Research, Faculty of Mathematics, Interdisciplinary Mathematical Insititute, Complutense University of Madrid, Plaza Ciencias, 3, 28040 Madrid, Spain.
Entropy (Basel). 2022 Apr 28;24(5):616. doi: 10.3390/e24050616.
The Rao's score, Wald and likelihood ratio tests are the most common procedures for testing hypotheses in parametric models. None of the three test statistics is uniformly superior to the other two in relation with the power function, and moreover, they are first-order equivalent and asymptotically optimal. Conversely, these three classical tests present serious robustness problems, as they are based on the maximum likelihood estimator, which is highly non-robust. To overcome this drawback, some test statistics have been introduced in the literature based on robust estimators, such as robust generalized Wald-type and Rao-type tests based on minimum divergence estimators. In this paper, restricted minimum Rényi's pseudodistance estimators are defined, and their asymptotic distribution and influence function are derived. Further, robust Rao-type and divergence-based tests based on minimum Rényi's pseudodistance and restricted minimum Rényi's pseudodistance estimators are considered, and the asymptotic properties of the new families of tests statistics are obtained. Finally, the robustness of the proposed estimators and test statistics is empirically examined through a simulation study, and illustrative applications in real-life data are analyzed.
拉奥得分检验、沃尔德检验和似然比检验是参数模型中检验假设最常用的方法。在功效函数方面，这三种检验统计量中没有一个在所有情况下都优于其他两个，而且，它们是一阶等价且渐近最优的。相反，这三种经典检验存在严重的稳健性问题，因为它们基于极大似然估计量，而极大似然估计量的稳健性很差。为克服这一缺点，文献中引入了一些基于稳健估计量的检验统计量，比如基于最小散度估计量的稳健广义沃尔德型检验和拉奥型检验。本文定义了受限最小雷尼伪距离估计量，并推导了它们的渐近分布和影响函数。此外，考虑了基于最小雷尼伪距离和受限最小雷尼伪距离估计量的稳健拉奥型检验和基于散度的检验，并得到了新的检验统计量族的渐近性质。最后，通过模拟研究对所提出估计量和检验统计量的稳健性进行了实证检验，并对实际数据中的示例应用进行了分析。
