Weak Order Partitioning of Interval Orders with Applications to Interval Censored Data

We propose a method by which the set of linear extensions of an interval order may be partitioned into sets of linear extensions of weak orders, using so-called marked conngurations of the interval order. The technique relies heavily on the natural linear ordering of maximal antichains in interval orders. We also propose a method whereby sets from this partition can be generated with known probability so as to permit eecient cluster or staged sampling. These techniques, among other uses, may be applied to generate sampling estimates of average rank score statistics for interval censored data similar in construction to that proposed by Prentice (1978) for right-censored data.