Robust regression with asymmetric loss functions
- 11 May 2021
- journal article
- research article
- Published by SAGE Publications in Statistical Methods in Medical Research
- Vol. 30 (8), 1800-1815
- https://doi.org/10.1177/09622802211012012
Abstract
In robust regression, it is usually assumed that the distribution of the error term is symmetric or the data are symmetrically contaminated by outliers. However, this assumption is usually not satisfied in practical problems, and thus if the traditional robust methods, such as Tukey’s biweight and Huber’s method, are used to estimate the regression parameters, the efficiency of the parameter estimation can be lost. In this paper, we construct an asymmetric Tukey’s biweight loss function with two tuning parameters and propose a data-driven method to find the most appropriate tuning parameters. Furthermore, we provide an adaptive algorithm to obtain robust and efficient parameter estimates. Our extensive simulation studies suggest that the proposed method performs better than the symmetric methods when error terms follow an asymmetric distribution or are asymmetrically contaminated. Finally, a cardiovascular risk factors dataset is analyzed to illustrate the proposed method.Funding Information
- the Natural Science Basic Research Plan in Shaanxi Province of China (2018JQ1006)
- Natural Science Foundation of Zhejiang Province (Y19A010054)
- the National Science Foundation of China (11871390)
- the Australian Research Council Discovery Project (DP160104292)
This publication has 12 references indexed in Scilit:
- Fully efficient robust estimation, outlier detection, and variable selection via penalized regressionStatistica Sinica, 2018
- Efficient Robust Regression via Two-Stage Generalized Empirical LikelihoodJournal of the American Statistical Association, 2013
- Robust Estimation Using the Huber Function With a Data-Dependent Tuning ConstantJournal of Computational and Graphical Statistics, 2007
- Robust estimation for linear regression with asymmetric errorsThe Canadian Journal of Statistics / La Revue Canadienne de Statistique, 2005
- Trimmed Least Squares Estimation in the Linear ModelJournal of the American Statistical Association, 1980
- On Estimating Variances of Robust Estimators When the Errors are AsymmetricJournal of the American Statistical Association, 1979
- Robust Estimation of a Location Parameter in the Presence of AsymmetryThe Annals of Statistics, 1976
- A Robust Method for Multiple Linear RegressionTechnometrics, 1974
- The Influence Curve and its Role in Robust EstimationJournal of the American Statistical Association, 1974
- Robust Estimates of Location: Symmetry and Asymmetric ContaminationThe Annals of Mathematical Statistics, 1971