The Min-Max Algorithm and Isotonic Regression

Abstract

There is growing interest in statistical inference under order restrictions. A major demand in this subject is to have a fast, direct method to solve the least squares problem of partially ordered isotonic regression. The Min-Max algorithm is such a method in which the user searches for the global minimum and the local maximum successively. A comparison of algorithms for partially ordered isotonic regression is included. As an application, using this efficient algorithm, it is feasible to approximate critical values of isotonic tests by simulation.