# Isotonic Regression

Speaker:

## Time:

Friday, 27 September 2013, 16:00 to 17:30

## Venue:

• D-405 (D-Block Seminar Room)

## Organisers:

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.