Journal
ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS
Volume 71, Issue 2, Pages 409-438Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s10463-018-0645-1
Keywords
Asymptotics; Expectile regression; Heteroscedasticity; Penalized regression; Variable selection
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Funding
- Basic Science Research Program through the National Research Foundation of Korea (NRF) - Ministry of Education [NRF-2013R1A1A2007611]
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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.
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