• Corpus ID: 226226784

# Enveloped Huber Regression.

@article{Zhou2020EnvelopedHR,
title={Enveloped Huber Regression.},
author={Le Zhou and R. Dennis Cook and Hui Zou},
journal={arXiv: Methodology},
year={2020}
}
• Published 30 October 2020
• Mathematics
• arXiv: Methodology
Huber regression (HR) is a popular robust alternative to the least squares regression when the error follows a heavy-tailed distribution. We propose a new method called the enveloped Huber regression (EHR) by considering the envelope assumption that there exists some subspace of the predictors that has no association with the response, which is referred to as the immaterial part. More efficient estimation is achieved via the removal of the immaterial part. Different from the envelope least…

## References

SHOWING 1-10 OF 39 REFERENCES
Envelope Quantile Regression
• Mathematics
• 2020
Quantile regression offers a valuable complement of classical mean regression for robust and comprehensive data analysis in a variety of applications. We propose a novel envelope quantile regression
Scaled envelopes: scale-invariant and efficient estimation in multivariate linear regression
• Mathematics
• 2013
Efficient estimation of the regression coefficients is a fundamental problem in multivariate linear regression. The envelope model proposed by Cook et al. (2010) was shown to have the potential to
Inner envelopes: Efficient estimation in multivariate linear regression
• Mathematics
• 2012
In this article we propose a new model, called the inner envelope model, which leads to efficient estimation in the context of multivariate normal linear regression. The asymptotic distribution and
Sparse envelope model: efficient estimation and response variable selection in multivariate linear regression
• Mathematics
• 2016
The envelope model allows efficient estimation in multivariate linear regression. In this paper, we propose the sparse envelope model, which is motivated by applications where some response variables
Sparse envelope model: efficient estimation and response variable selection in multivariate linear regression
The envelope model allows efficient estimation in multivariate linear regression. In this paper, we propose the sparse envelope model, which is motivated by applications where some response variables
Partial Envelopes for Efficient Estimation in Multivariate Linear Regression
We introduce the partial envelope model, which leads to a par simonious method for multivariate linear regression when some of the predictors are of special interest. It has the potential to achieve
A Bayesian approach for envelope models
• Computer Science
• 2017
A comprehensive Bayesian framework for estimation and model selection in envelope models in the context of multivariate linear regression is developed and can accommodate situations where the sample size is smaller than the number of responses.
ENVELOPE MODELS FOR PARSIMONIOUS AND EFFICIENT MULTIVARIATE LINEAR REGRESSION
• Mathematics
• 2010
We propose a new parsimonious version of the classical multivariate nor- mal linear model, yielding a maximum likelihood estimator (MLE) that is asymp- totically less variable than the MLE based on
New Parsimonious Multivariate Spatial Model: Spatial Envelope
• Mathematics
• 2017
Dimension reduction provides a useful tool for analyzing high dimensional data. The recently developed \textit{Envelope} method is a parsimonious version of the classical multivariate regression
Quantile Regression for Analyzing Heterogeneity in Ultra-High Dimension
• Computer Science
Journal of the American Statistical Association
• 2012
A novel, sufficient optimality condition that relies on a convex differencing representation of the penalized loss function and the subdifferential calculus is introduced that enables the oracle property for sparse quantile regression in the ultra-high dimension under relaxed conditions.