A note on the conditional Markov property of discrete order statistics (Q1067318)

Order statistics, in general, do not have the Markov property if the sample comes from a discrete distribution. The paper proves that conditioned on certain events based on order statistics themselves, the order statistics will have the Markov property. Reviewer's remark: If \(X_ 1\leq X_ 2\leq...\leq X_ n\) is the order statistics and \(a_ k\) denotes the number of those \(X_ i's\) for which \(i\leq k\) and \(X_ i=X_ k\) then \((X_ k,a_ k)\), \(k=1,2,...,n\) form a Markov chain.