Testing Ordered Alternatives in the Presence of Incomplete Data
针对随机区组实验中存在缺失数据的情况，推广了Jonckheere和Page基于秩相关的检验方法，证明了新统计量的渐近正态性，并发现扩展Page检验的效率损失不大。
Abstract In testing the null hypothesis of no treatment effects in a randomized block experiment, a researcher may restrict attention to an ordered alternative and thereby increase the power of his test. Jonckheere and later Page proposed such test statistics based on the Kendall and Spearman correlation coefficients. Motivated by notions of distance between permutations, we generalize Jonckheere's and Page's tests to the situation in which one or more observations are missing from one or more blocks. Conditional on the pattern of missing observations, the resulting statistics are shown to be asymptotically normal. For a particular pattern of missing observations, the asymptotic efficiency of the extended Page test is found, in many cases, to be not much lower than for the standard Page test. Key Words: Jonckheere testMissing observationsPage testRandomized blockRank correlation