Displaying similar documents to “A new large deviation inequality for U -statistics of order 2 ”

Adaptive estimation of a quadratic functional of a density by model selection

Béatrice Laurent (2005)

ESAIM: Probability and Statistics

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We consider the problem of estimating the integral of the square of a density f from the observation of a n sample. Our method to estimate ∫ ℝ f 2 ( x ) d x is based on model selection via some penalized criterion. We prove that our estimator achieves the adaptive rates established by Efroimovich and Low on classes of smooth functions. A key point of the proof is an exponential inequality for U -statistics of order 2 due to Houdré and Reynaud.

Detecting abrupt changes in random fields

Antoine Chambaz (2002)

ESAIM: Probability and Statistics

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This paper is devoted to the study of some asymptotic properties of a M -estimator in a framework of detection of abrupt changes in random field’s distribution. This class of problems includes e.g. recovery of sets. It involves various techniques, including M -estimation method, concentration inequalities, maximal inequalities for dependent random variables and φ -mixing. Penalization of the criterion function when the size of the true model is unknown is performed. All the results apply...