Nandy Amarnath, Basu Ayanendranath, Ghosh Abhik
Interdisciplinary Statistical Research Unit, Indian Statistical Institute, Kolkata, India.
J Appl Stat. 2021 Feb 25;49(8):2093-2123. doi: 10.1080/02664763.2021.1891527. eCollection 2022.
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.
健康数据往往不具有对称性，无法通过通常的正态分布进行充分建模；其中大多数呈现出偏态模式。实际上，通过涵盖偏态和对称情况的更广泛的偏态正态分布族，能够对它们进行更好的建模。由于在复杂的现实生活实验数据集中异常值并不罕见，一种能够自动处理数据中的噪声的稳健方法对于产生稳定且更精确的研究见解从而制定更好的政策具有很大的实用价值。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估计器和检验程序，并将其应用于健康数据。特别地，讨论了在存在异常值的情况下检验对称性的稳健程序。还讨论了两种有效的计算算法。除了推导所提出方法的渐近性和稳健性理论外，还通过模拟以及对来自澳大利亚体育学院的运动员健康数据和艾滋病临床试验数据的一些实际应用，说明了它们的优势和效用。
