- Robust Sure Independence Screening for Ultrahigh Dimensional
Non-normal Data
- Wei Zhong
- Acta Mathematica Sinica Vol. 30, No. 11, pp. 1885–1896
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- Sure independence screening (SIS) has been proposed to reduce the ultrahigh dimensionality
down to a moderate scale and proved to enjoy the sure screening property under Gaussian linear
models. However, the observed response is often skewed or heavy-tailed with extreme values in practice,
which may dramatically deteriorate the performance of SIS. To this end, we propose a new robust sure
independence screening (RoSIS) via considering the correlation between each predictor and the distribution
function of the response. The proposed approach contributes to the literature in the following
three folds: First, it is able to reduce ultrahigh dimensionality effectively. Second, it is robust to heavy
tails or extreme values in the response. Third, it possesses both sure screening property and ranking
consistency property under milder conditions. Furthermore, we demonstrate its excellent finite sample
performance through numerical simulations and a real data example.
- JEL-Codes:
- Keywords: Robustness, sure independence screening, sure screening property, ultrahigh dimensionality, variable selection
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