ABSTRACT

Health data are often not symmetric to be adequately modeled through the usual normal distributions; most of them exhibit skewed patterns. They can indeed be modeled better through the larger family of skew-normal distributions covering both skewed and symmetric cases. Since outliers are not uncommon in complex real-life experimental datasets, a robust methodology automatically taking care of the noises in the data would be of great practical value to produce stable and more precise research insights leading to better policy formulation. In this paper, we develop a class of robust estimators and testing procedures for the family of skew-normal distributions using the minimum density power divergence approach with application to health data. In particular, a robust procedure for testing of symmetry is discussed in the presence of outliers. Two efficient computational algorithms are discussed. Besides deriving the asymptotic and robustness theory for the proposed methods, their advantages and utilities are illustrated through simulations and a couple of real-life applications for health data of athletes from Australian Institute of Sports and AIDS clinical trial data.

摘要

健康数据通常不是对称的，无法通过通常的正态分布进行充分建模；他们中的大多数表现出倾斜的模式。它们确实可以通过涵盖倾斜和对称情况的更大的倾斜正态分布族更好地建模。由于异常值在复杂的现实生活实验数据集中并不少见，因此一种自动处理数据中噪声的稳健方法对于产生稳定和更精确的研究洞察力从而更好地制定政策具有重要的实用价值。在本文中，我们使用最小密度功率散度方法为偏态正态分布族开发了一类稳健的估计器和测试程序，并将其应用于健康数据。特别是，在存在异常值的情况下讨论了用于测试对称性的稳健程序。讨论了两种有效的计算算法。除了为所提出的方法推导渐近和鲁棒性理论外，它们的优势和实用性还通过模拟和澳大利亚体育研究所和艾滋病临床试验数据的运动员健康数据的几个实际应用来说明。