Some applications of concentration inequalities to statistics
Pascal Massart (2000)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Pascal Massart (2000)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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K. Bertin, E. Le Pennec, V. Rivoirard (2011)
Annales de l'I.H.P. Probabilités et statistiques
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The aim of this paper is to build an estimate of an unknown density as a linear combination of functions of a dictionary. Inspired by Candès and Tao’s approach, we propose a minimization of the 1-norm of the coefficients in the linear combination under an adaptive Dantzig constraint coming from sharp concentration inequalities. This allows to consider a wide class of dictionaries. Under local or global structure assumptions, oracle inequalities are derived. These theoretical results...
Pascal Massart (2002)
Annales de l'I.H.P. Probabilités et statistiques
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Evarist Giné, Armelle Guillou (2002)
Annales de l'I.H.P. Probabilités et statistiques
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Vladimir Koltchinskii (2003)
Annales de l'I.H.P. Probabilités et statistiques
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Vladimir Koltchinskii (2009)
Annales de l'I.H.P. Probabilités et statistiques
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Let (, ) be a random couple in × with unknown distribution . Let ( , ), …, ( , ) be i.i.d. copies of (, ), being their empirical distribution. Let , …, :↦[−1, 1] be a dictionary consisting of functions. For ∈ℝ, denote :=∑ . Let :×ℝ↦ℝ be a given loss function, which is convex with...