Penalized expectile regression: an alternative to penalized quantile regression

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This paper concerns the study of the entire conditional distribution of a response given predictors in a heterogeneous regression setting. A common approach to address heterogeneous data is quantile regression, which utilizes the minimization of the L1 norm. As an alternative to quantile regression, we consider expectile regression, which relies on the minimization of the asymmetric L2 norm and detects heteroscedasticity effectively. We assume that only a small set of predictors is relevant to the response and develop penalized expectile regression with SCAD and adaptive LASSO penalties. With properly chosen tuning parameters, we show that the proposed estimators display oracle properties. A numerical study using simulated and real examples demonstrates the competitive performance of the proposed penalized expectile regression, and its combined use with penalized quantile regression would be helpful and recommended for practitioners.
Publisher
SPRINGER HEIDELBERG
Issue Date
2019-04
Language
English
Article Type
Article
Citation

ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, v.71, no.2, pp.409 - 438

ISSN
0020-3157
DOI
10.1007/s10463-018-0645-1
URI
http://hdl.handle.net/10203/285771
Appears in Collection
MA-Journal Papers(저널논문)
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