Various estimators have been proposed to estimate conditional expectiles, including those from multiple linear expectile regression, local polynomial expectile regression, boosted expectile regression, and so on. It is a common practice that several plausible candidate estimators are fitted and a final estimator is selected from the candidate list. In this article, we advocate the use of an exponential weighting scheme to adaptively aggregate the candidate estimators into a final estimator. We show oracle inequalities for the aggregated estimator. Simulations and data examples demonstrate that the aggregated estimator could have substantial gain in accuracy under both squared and asymmetric squared errors.
Bibliographical noteFunding Information:
The authors thank the Editor, an associate editor, and four reviewers for their insightful comments and suggestions that have helped us improve the quality of the paper substantially. This work is supported in part by NSF grant DMS-1505111.
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- Expectile regression
- Model aggregation
- Oracle inequality