Nonparametric multiple expectile regression via ER-Boost

Yi Yang, Hui Zou

Research output: Contribution to journalArticlepeer-review

27 Scopus citations

Abstract

Expectile regression [Newey W, Powell J. Asymmetric least squares estimation and testing, Econometrica. 1987;55:819–847] is a nice tool for estimating the conditional expectiles of a response variable given a set of covariates. Expectile regression at 50% level is the classical conditional mean regression. In many real applications having multiple expectiles at different levels provides a more complete picture of the conditional distribution of the response variable. Multiple linear expectile regression model has been well studied [Newey W, Powell J. Asymmetric least squares estimation and testing, Econometrica. 1987;55:819–847; Efron B. Regression percentiles using asymmetric squared error loss, Stat Sin. 1991;1(93):125.], but it can be too restrictive for many real applications. In this paper, we derive a regression tree-based gradient boosting estimator for nonparametric multiple expectile regression. The new estimator, referred to as ER-Boost, is implemented in an R package erboost publicly available at http://cran.r-project.org/web/packages/erboost/index.html. We use two homoscedastic/heteroscedastic random-function-generator models in simulation to show the high predictive accuracy of ER-Boost. As an application, we apply ER-Boost to analyse North Carolina County crime data. From the nonparametric expectile regression analysis of this dataset, we draw several interesting conclusions that are consistent with the previous study using the economic model of crime. This real data example also provides a good demonstration of some nice features of ER-Boost, such as its ability to handle different types of covariates and its model interpretation tools.

Original languageEnglish (US)
Pages (from-to)1442-1458
Number of pages17
JournalJournal of Statistical Computation and Simulation
Volume85
Issue number7
DOIs
StatePublished - May 3 2015
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2014, © 2014 Taylor & Francis.

Keywords

  • asymmetric least squares
  • expectile regression
  • functional gradient descent
  • gradient boosting
  • regression tree

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