The Annals of Statistics
- Ann. Statist.
- Volume 40, Number 4 (2012), 2327-2355.
Sharp oracle inequalities for aggregation of affine estimators
We consider the problem of combining a (possibly uncountably infinite) set of affine estimators in nonparametric regression model with heteroscedastic Gaussian noise. Focusing on the exponentially weighted aggregate, we prove a PAC-Bayesian type inequality that leads to sharp oracle inequalities in discrete but also in continuous settings. The framework is general enough to cover the combinations of various procedures such as least square regression, kernel ridge regression, shrinking estimators and many other estimators used in the literature on statistical inverse problems. As a consequence, we show that the proposed aggregate provides an adaptive estimator in the exact minimax sense without discretizing the range of tuning parameters or splitting the set of observations. We also illustrate numerically the good performance achieved by the exponentially weighted aggregate.
Ann. Statist., Volume 40, Number 4 (2012), 2327-2355.
First available in Project Euclid: 23 January 2013
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Dalalyan, Arnak S.; Salmon, Joseph. Sharp oracle inequalities for aggregation of affine estimators. Ann. Statist. 40 (2012), no. 4, 2327--2355. doi:10.1214/12-AOS1038. https://projecteuclid.org/euclid.aos/1358951384
- Supplementary material: Proofs of some propositions. In this supplement we present the detailed proofs of Propositions 2–6.