Davidov Ori, Peddada Shyamal
Department of Statistics, University of Haifa, Mount Carmel, Haifa 31905 Israel.
Ann Stat. 2013 Feb 1;41(1):1-40. doi: 10.1214/12-AOS1062.
Researchers are often interested in drawing inferences regarding the order between two experimental groups on the basis of multivariate response data. Since standard multivariate methods are designed for two sided alternatives they may not be ideal for testing for order between two groups. In this article we introduce the notion of the linear stochastic order and investigate its properties. Statistical theory and methodology are developed to both estimate the direction which best separates two arbitrary ordered distributions and to test for order between the two groups. The new methodology generalizes Roy's classical largest root test to the nonparametric setting and is applicable to random vectors with discrete and/or continuous components. The proposed methodology is illustrated using data obtained from a 90-day pre-chronic rodent cancer bioassay study conducted by the National Toxicology Program (NTP).
研究人员常常希望基于多变量响应数据对两个实验组之间的顺序进行推断。由于标准的多变量方法是为双侧备择假设设计的，所以它们可能并不适合用于检验两组之间的顺序。在本文中，我们引入了线性随机序的概念并研究其性质。我们开发了统计理论和方法，用于估计能最佳区分两个任意有序分布的方向，并检验两组之间的顺序。新方法将罗伊的经典最大根检验推广到了非参数情形，适用于具有离散和/或连续分量的随机向量。本文使用从美国国家毒理学计划（NTP）进行的一项为期90天的慢性啮齿动物癌症生物测定预实验研究中获得的数据，对所提出的方法进行了说明。
