Bounded isotonic regression
type: Item
instance of: scholarly article
title: Bounded isotonic regression
zbMATH Open document ID: 1383.62119
DOI: 10.1214/17-EJS1365
author: Ronny Luss
author: Saharon Rosset
published in: Electronic Journal of Statistics
publication date: 2017-12-08T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.ejs/1510887944
review text: Let \(\{(x_1,y_1),\ldots,(x_n,y_n)\}\) be a set of observations each consisting of a vector of covariates \(x\in\mathcal{X}\) and a response \(y\in\mathbb{R}\). It is supposed that the covariate space is equipped with a partial order \(\preceq\). The class of isotonic models \(\mathcal{G}\) is defined as the collection of models \(g:\mathcal{X}\rightarrow \mathbb{R}\) having the following property \[ x,z\in\mathcal{X}, x\preceq z \;\Rightarrow\;g(x)\leq g(z). \] The authors of the paper resent the bounded isotonic regression (BIR) model which can be presented by the formula \[ \hat{g}=\text{argmin}_{g\in\mathcal{G}, \operatorname{range}(g)\leq s}\;\sum\limits_{i=1}^n\big(y_i-g(x_i)\big)^2, \] where \[ \operatorname{range}(g)=\sup\limits_{x\in\mathcal{X}} g(x)-\inf\limits_{x\in\mathcal{X}}g(x). \] The properties of the BIR model are presented and the algorithm to find this model is described. It is shown that the BIR algorithm can be easily generalized to other loss functions. The favorable empirical performance of the presented approach compared to various relevant alternatives is demonstrated.
reviewed by: Jonas Šiaulys
Mathematics Subject Classification ID: 62G08
Mathematics Subject Classification ID: 62J07
Mathematics Subject Classification ID: 62H12
zbMATH DE Number: 6816623
zbMATH Keywords: isotonic regression
zbMATH Keywords: multivariate regression
zbMATH Keywords: bounded regression
zbMATH Keywords: nonparametric regression
zbMATH Keywords: optimal threshold
zbMATH Keywords: range regularization
zbMATH Keywords: Lasso regularization
zbMATH Keywords: partial order
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6816623