Adaptive robust regression with continuous Gaussian scale mixture errors

Byungtae Seo, Jungsik Noh, Taewook Lee, Young Joo Yoon

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Model based regression analysis always requires a certain choice of models which typically specifies the behavior of regression errors. The normal distribution is the most common choice for this purpose, but the estimator under normality is known to be too sensitive to outliers. As an alternative, heavy tailed distributions such as t distributions have been suggested. Though this choice can reduce the sensitivity to outliers, it also requires the choice of distributions and tuning parameters for practical use. In this paper, we propose a class of continuous Gaussian scale mixtures for the error distribution that contains most symmetric unimodal probability distributions including normal, t, Laplace, and stable distributions. With this quite flexible class of error distributions, we provide the asymptotic property and robust property of the proposed method, and show its successes along with numerical examples.

Original languageEnglish (US)
Pages (from-to)113-125
Number of pages13
JournalJournal of the Korean Statistical Society
Volume46
Issue number1
DOIs
StatePublished - Mar 1 2017

Fingerprint

Scale Mixture
Robust Regression
Gaussian Mixture
t-distribution
Outlier
Gaussian distribution
Unimodal Distribution
Laplace Distribution
Heavy-tailed Distribution
Stable Distribution
Parameter Tuning
Regression Analysis
Normality
Asymptotic Properties
Probability Distribution
Regression
Model-based
Estimator
Numerical Examples
Alternatives

Keywords

  • Adaptive robust regression
  • Asymptotics
  • Continuous scale Gaussian mixture
  • M-estimation

ASJC Scopus subject areas

  • Statistics and Probability

Cite this

Adaptive robust regression with continuous Gaussian scale mixture errors. / Seo, Byungtae; Noh, Jungsik; Lee, Taewook; Yoon, Young Joo.

In: Journal of the Korean Statistical Society, Vol. 46, No. 1, 01.03.2017, p. 113-125.

Research output: Contribution to journalArticle

Seo, Byungtae ; Noh, Jungsik ; Lee, Taewook ; Yoon, Young Joo. / Adaptive robust regression with continuous Gaussian scale mixture errors. In: Journal of the Korean Statistical Society. 2017 ; Vol. 46, No. 1. pp. 113-125.
@article{eba529fcbafc47d4a2071c9a7c2761a2,
title = "Adaptive robust regression with continuous Gaussian scale mixture errors",
abstract = "Model based regression analysis always requires a certain choice of models which typically specifies the behavior of regression errors. The normal distribution is the most common choice for this purpose, but the estimator under normality is known to be too sensitive to outliers. As an alternative, heavy tailed distributions such as t distributions have been suggested. Though this choice can reduce the sensitivity to outliers, it also requires the choice of distributions and tuning parameters for practical use. In this paper, we propose a class of continuous Gaussian scale mixtures for the error distribution that contains most symmetric unimodal probability distributions including normal, t, Laplace, and stable distributions. With this quite flexible class of error distributions, we provide the asymptotic property and robust property of the proposed method, and show its successes along with numerical examples.",
keywords = "Adaptive robust regression, Asymptotics, Continuous scale Gaussian mixture, M-estimation",
author = "Byungtae Seo and Jungsik Noh and Taewook Lee and Yoon, {Young Joo}",
year = "2017",
month = "3",
day = "1",
doi = "10.1016/j.jkss.2016.08.002",
language = "English (US)",
volume = "46",
pages = "113--125",
journal = "Journal of the Korean Statistical Society",
issn = "1226-3192",
publisher = "Korean Statistical Society",
number = "1",

}

TY - JOUR

T1 - Adaptive robust regression with continuous Gaussian scale mixture errors

AU - Seo, Byungtae

AU - Noh, Jungsik

AU - Lee, Taewook

AU - Yoon, Young Joo

PY - 2017/3/1

Y1 - 2017/3/1

N2 - Model based regression analysis always requires a certain choice of models which typically specifies the behavior of regression errors. The normal distribution is the most common choice for this purpose, but the estimator under normality is known to be too sensitive to outliers. As an alternative, heavy tailed distributions such as t distributions have been suggested. Though this choice can reduce the sensitivity to outliers, it also requires the choice of distributions and tuning parameters for practical use. In this paper, we propose a class of continuous Gaussian scale mixtures for the error distribution that contains most symmetric unimodal probability distributions including normal, t, Laplace, and stable distributions. With this quite flexible class of error distributions, we provide the asymptotic property and robust property of the proposed method, and show its successes along with numerical examples.

AB - Model based regression analysis always requires a certain choice of models which typically specifies the behavior of regression errors. The normal distribution is the most common choice for this purpose, but the estimator under normality is known to be too sensitive to outliers. As an alternative, heavy tailed distributions such as t distributions have been suggested. Though this choice can reduce the sensitivity to outliers, it also requires the choice of distributions and tuning parameters for practical use. In this paper, we propose a class of continuous Gaussian scale mixtures for the error distribution that contains most symmetric unimodal probability distributions including normal, t, Laplace, and stable distributions. With this quite flexible class of error distributions, we provide the asymptotic property and robust property of the proposed method, and show its successes along with numerical examples.

KW - Adaptive robust regression

KW - Asymptotics

KW - Continuous scale Gaussian mixture

KW - M-estimation

UR - http://www.scopus.com/inward/record.url?scp=84994845924&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84994845924&partnerID=8YFLogxK

U2 - 10.1016/j.jkss.2016.08.002

DO - 10.1016/j.jkss.2016.08.002

M3 - Article

AN - SCOPUS:84994845924

VL - 46

SP - 113

EP - 125

JO - Journal of the Korean Statistical Society

JF - Journal of the Korean Statistical Society

SN - 1226-3192

IS - 1

ER -