Open Access
April 2012 Kullback–Leibler aggregation and misspecified generalized linear models
Philippe Rigollet
Ann. Statist. 40(2): 639-665 (April 2012). DOI: 10.1214/11-AOS961


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.


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Philippe Rigollet. "Kullback–Leibler aggregation and misspecified generalized linear models." Ann. Statist. 40 (2) 639 - 665, April 2012.


Published: April 2012
First available in Project Euclid: 17 May 2012

zbMATH: 1274.62298
MathSciNet: MR2933661
Digital Object Identifier: 10.1214/11-AOS961

Primary: 62G08
Secondary: 62F11 , 62J12 , 68T05

Keywords: Aggregation , ‎classification‎ , finite sample bounds , generalized linear models , logistic regression , minimax lower bounds , Oracle inequalities , regression

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.40 • No. 2 • April 2012
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