AN ALGORITHM FOR ISOTONIC REGRESSION WITH ARBITRARY CONVEX DISTANCE FUNCTION

In the present paper we consider the isotonic regression problem with an arbitrary convex distance function d(.), and the main purpose being to present an algorithm for obtaining all isotonic regressions under this reasonable assumption on d(.). Further, we consider a piece-wise linear distance function d(.) of the type d(t) = C-\t\ for t < 0 and d(t) = C+ \t\ for t greater-than-or-equal-to 0 and get an isotonic pth frctile regression by choosing p = C+ /(C- + C+).