Isotonic Regression

Abtract: In statistical analysis,  regression is a widely used tool to get a functional relationship between observations of a response variable Y and covariate X. The goal is to estimate the regression function $$ m(X)=E[Y|X] $$ The estimation of m(·) is done by least-squares, where m(·) is an arbitrary function. In isotonic regression we restrict the function m(·) to be monotone. In this talk, we will look at a  geometrical method to find m(·)  and prove its optimality. This method leads to fast algorithm called Pooled Adjacent Value Algorithm (PAVA) which is widely used in statistical packages.