Sharp oracle bounds for monotone and convex regression through aggregation

Pierre Bellec () and Alexandre Tsybakov ()
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Pierre Bellec: CREST, ENSAE, UMR CNRS 9194
Alexandre Tsybakov: CREST, ENSAE, UMR CNRS 9194

No 2015-04, Working Papers from Center for Research in Economics and Statistics

Abstract: We derive oracle inequalities for the problems of isotonic and convex regression using the combination of Q-aggregation procedure and sparsity pattern aggregation. This improves upon the previous results including the oracle inequalities for the constrained least squares estimator. One of the improvements is that our oracle inequalities are sharp, i.e., with leading constant 1. It allows us to obtain bounds for the minimax regret thus accounting for model misspecification, which was not possible based on the previous results. Another improvement is that we obtain oracle inequalities both with high probability and in expectation.

Pages: 17
Date: 2015-07
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Citations: View citations in EconPapers (1)

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