INVARIANT DIRECTIONAL ORDERINGS

• 成果类型: Article
• 署名作者: LEHMANN, EL; ROJO, J
• 署名单位: University of Texas System; University of Texas El Paso
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176348905
• 发表日期: 1992
• 页码: 2100-2110
• 关键词: conditional stochastic order; distributions; skewness

摘要

Statistical concepts of order permeate the theory and practice of statistics. The present paper is concerned with a large class of directional orderings of univariate distributions. (What do we mean by saying that a random variable Y is larger than another random variable X?) Attention is restricted to preorders that are invariant under monotone transformations; this includes orderings such as monotone likelihood ratio, hazard ordering, and stochastic ordering. Simple characterizations of these orderings are obtained in terms of a maximal invariant. It is shown how such invariant preorderings can be used to generate concepts of Y2 being further to the right of X2 than Y1 is of X1.