2009/11/30 by Philippe Rigollet · 38 citations
Computer Science · Mathematics · #Advanced Statistical Methods and Models #Bayesian Modeling and Causal Inference #Component (thermodynamics) #Distribution (mathematics) #Exponential function #Extension (predicate logic) #Generalized linear model #Identifiability #Linear model #Maximization #Minimax #Statistical Methods and Bayesian Inference #math.ST #stat.ML #stat.TH
paper · pdf · doi:10.1214/11-aos961
published in The Annals of Statistics 40(2) (Institute of Mathematical Statistics) · Published in at http://dx.doi.org/10.1214/11-AOS961 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2012/04/01 · arxiv created 2012/06/05 · arxiv updated 2012/06/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.