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Aggregation of affine estimators

Author(s): Dai, Dong; Rigollet, Philippe; Xia, Lucy; Zhang, Tong

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dc.contributor.authorDai, Dong-
dc.contributor.authorRigollet, Philippe-
dc.contributor.authorXia, Lucy-
dc.contributor.authorZhang, Tong-
dc.date.accessioned2020-03-02T23:42:49Z-
dc.date.available2020-03-02T23:42:49Z-
dc.date.issued2014en_US
dc.identifier.citationDai, Dong, Rigollet, Philippe, Xia, Lucy, Zhang, Tong. (2014). Aggregation of affine estimators. Electronic Journal of Statistics, 8 (1), 302 - 327. doi:10.1214/14-EJS886en_US
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr1jv3z-
dc.description.abstractWe consider the problem of aggregating a general collection of affine estimators for fixed design regression. Relevant examples include some commonly used statistical estimators such as least squares, ridge and robust least squares estimators. Dalalyan and Salmon [DS12] have established that, for this problem, exponentially weighted (EW) model selection aggregation leads to sharp oracle inequalities in expectation, but similar bounds in deviation were not previously known. While results [DRZ12] indicate that the same aggregation scheme may not satisfy sharp oracle inequalities with high probability, we prove that a weaker notion of oracle inequality for EW that holds with high probability. Moreover, using a generalization of the newly introduced Q-aggregation scheme we also prove sharp oracle inequalities that hold with high probability. Finally, we apply our results to universal aggregation and show that our proposed estimator leads simultaneously to all the best known bounds for aggregation, including ℓq-aggregation, q ∈ (0, 1), with high probability.en_US
dc.format.extent302 - 327en_US
dc.language.isoen_USen_US
dc.relation.ispartofElectronic Journal of Statisticsen_US
dc.rightsFinal published version. This is an open access article.en_US
dc.titleAggregation of affine estimatorsen_US
dc.typeJournal Articleen_US
dc.identifier.doidoi:10.1214/14-EJS886-
dc.identifier.eissn1935-7524-
pu.type.symplectichttp://www.symplectic.co.uk/publications/atom-terms/1.0/journal-articleen_US

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