Isotonic regression on permutations
H. W. Block, S. Qian, Allan R. Sampson · Lecture notes-monograph series · 1996
Motivated by an approach to qualifying potential judges, we study isotonic regression problems on a partially ordered set of permutations.We consider the partial orders discussed in Block, Chhetry, Fang and Sampson (1990) which are used for comparing the dependence of bivariate empirical distributions with fixed marginals.We give a method to generate permutations and their inversion numbers, and develop a technique to input these orders.We discuss methods of finding predecessors and immediate predecessors in the sense of these orders.Then, we develop an algorithm to search for isotonic regressions on a set of permutations under these orders.