Castilla Elena, Ghosh Abhik, Martin Nirian, Pardo Leandro
Department of Statistics, Complutense University of Madrid, 28040 Madrid, Spain.
Indian Statistical Institute, Kolkata, India.
Biometrics. 2018 Dec;74(4):1282-1291. doi: 10.1111/biom.12890. Epub 2018 May 17.
This article derives a new family of estimators, namely the minimum density power divergence estimators, as a robust generalization of the maximum likelihood estimator for the polytomous logistic regression model. Based on these estimators, a family of Wald-type test statistics for linear hypotheses is introduced. Robustness properties of both the proposed estimators and the test statistics are theoretically studied through the classical influence function analysis. Appropriate real life examples are presented to justify the requirement of suitable robust statistical procedures in place of the likelihood based inference for the polytomous logistic regression model. The validity of the theoretical results established in the article are further confirmed empirically through suitable simulation studies. Finally, an approach for the data-driven selection of the robustness tuning parameter is proposed with empirical justifications.
本文推导了一类新的估计量，即最小密度功率散度估计量，作为多分类逻辑回归模型最大似然估计量的稳健推广。基于这些估计量，引入了一类用于线性假设的 Wald 型检验统计量。通过经典影响函数分析，从理论上研究了所提出的估计量和检验统计量的稳健性。给出了适当的实际例子，以证明对于多分类逻辑回归模型，需要合适的稳健统计程序来替代基于似然的推断。通过适当的模拟研究，进一步从经验上证实了本文所建立理论结果的有效性。最后，提出了一种数据驱动的稳健性调整参数选择方法，并给出了经验依据。
