Contributions to the Theory of Rank Order Statistics: The Two-Sample Censored Case

Abstract

Rank order theory is developed for the two-sample problem in which censoring of the observations has occurred, i.e., not all of the random variables are observed. The approach is similar to [2] with the striking difference that in the present case the rank orders are not all equally likely under the null hypothesis, and thus it becomes important to work with the likelihood ratios of rank orders. In applying the results of this paper, there will be a strong analogy to sequential analysis. The censoring scheme corresponds to the stopping rule and in both cases the terminal decision should be based on the likelihood ratio. We do not give the detailed applications of the present theory either to earlier procedures or to the new ones introduced here.