Isotonic Regression And The Application Research

In statistical analysis, statistical deduce under order restriction becomes an important constituent part because of it's profound application background. Isotonic regression research is the key to statistical deduce under order restriction. Maximum Likelihood Estimate(MLE) is a widely used estimate method in statistical analysis, which has many good estimate properties. Above all, we investigate Isotonic Regression through the relation between isotonic regression and MLE. So which are discussed in this paper as follow:1. It consider the resolution of Isotonic Regression by view of constraint optimization, and it also presents the relation between Isotonic Regression and MLE in detail.2. It considers the statistical property of Isotonic Regression that is started with the statistical property of MLE.3. We compare the result calculated by solving method for Isotonic Regression with MATLAB that we proposed with the result calculated by PAVA.4.It extend to the Isotonic Regression to multiple Isotonic Regression and generalized Isotonic Regression, this broaden the study area of Isotonic Regression. All of this for discussing other problems further is also useful.