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
N1 - Funding Information:
We thank the editor, associate editor, and two referees for their helpful comments and suggestions that have led to significant improvements of this paper. Young Joo Yoon’s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (Ministry of Science, ICT & Future Planning) (No. NRF-2014R1A1A1005049 ). The research of Byungtae Seo was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( NRF-2013R1A1A2057715 ).
Publisher Copyright:
© 2016 The Korean Statistical Society
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
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U2 - 10.1016/j.jkss.2016.08.002
DO - 10.1016/j.jkss.2016.08.002
M3 - Article
AN - SCOPUS:84994845924
SN - 1226-3192
VL - 46
SP - 113
EP - 125
JO - Journal of the Korean Statistical Society
JF - Journal of the Korean Statistical Society
IS - 1
ER -