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2019 Additive monotone regression in high and lower dimensions
Solveig Engebretsen, Ingrid K. Glad
Statist. Surv. 13: 1-51 (2019). DOI: 10.1214/19-SS124


In numerous problems where the aim is to estimate the effect of a predictor variable on a response, one can assume a monotone relationship. For example, dose-effect models in medicine are of this type. In a multiple regression setting, additive monotone regression models assume that each predictor has a monotone effect on the response. In this paper, we present an overview and comparison of very recent frequentist methods for fitting additive monotone regression models. Three of the methods we present can be used both in the high dimensional setting, where the number of parameters $p$ exceeds the number of observations $n$, and in the classical multiple setting where $1<p\leq n$. However, many of the most recent methods only apply to the classical setting. The methods are compared through simulation experiments in terms of efficiency, prediction error and variable selection properties in both settings, and they are applied to the Boston housing data. We conclude with some recommendations on when the various methods perform best.


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Solveig Engebretsen. Ingrid K. Glad. "Additive monotone regression in high and lower dimensions." Statist. Surv. 13 1 - 51, 2019.


Received: 1 November 2018; Published: 2019
First available in Project Euclid: 20 June 2019

zbMATH: 07080019
MathSciNet: MR3968232
Digital Object Identifier: 10.1214/19-SS124

Primary: 62G08

Keywords: additive regression , monotone regression , regression splines , shape constrained regression


Vol.13 • 2019
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