Algorithms and error estimations for monotone regression on partially preordered sets

Monotone (or isotonic) regression plays an important role in data analysis and in other fields. In many cases the monotonicity is only defined for a partial instead of a total preorder. No efficient algorithm is known which solves the general problem in a finite number of steps. For an approximate solution of the optimum some error estimations are given. Moreover, some new results concerning monotone regression and the treatment of missing values are presented in this paper.