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Kullback–Leibler aggregation and misspecified generalized linear models

Author(s): Rigollet, Philippe

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Abstract: In a regression setup with deterministic design, we study the pure aggregation problem and introduce a natural extension from the Gaussian distribution to distributions in the exponential family. While this extension bears strong connections with generalized linear models, it does not require identifiability of the parameter or even that the model on the systematic component is true. It is shown that this problem can be solved by constrained and/or penalized likelihood maximization and we derive sharp oracle inequalities that hold both in expectation and with high probability. Finally all the bounds are proved to be optimal in a minimax sense.
Publication Date: Apr-2012
Citation: Rigollet, Philippe. (2012). Kullback–Leibler aggregation and misspecified generalized linear models. The Annals of Statistics, 40 (2), 639 - 665. doi:10.1214/11-AOS961
DOI: doi:10.1214/11-AOS961
ISSN: 0090-5364
Pages: 639 - 665
Type of Material: Journal Article
Journal/Proceeding Title: The Annals of Statistics
Version: Author's manuscript

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