文章基本信息

标题：Aggregation of affine estimators
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作者：Dong Dai ; Philippe Rigollet ; Lucy Xia 等
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2014
卷号：8
期号：1
页码：302-327
DOI：10.1214/14-EJS886
语种：English
出版社：Institute of Mathematical Statistics
摘要：We 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 $\ell_{q}$-aggregation, $q\in(0,1)$, with high probability.