EXPONENTIAL INEQUALITY FOR CHAOS BASED ON SAMPLING WITHOUT REPLACEMENT

P Hodara (1) , Patricia Reynaud-Bouret (2)

1 INRA - Institut National de la Recherche Agronomique
2 LJAD - Laboratoire Jean Alexandre Dieudonné

We are interested in the behavior of particular functionals, in a framework where the only source of randomness is a sampling without replacement. More precisely the aim of this short note is to prove an exponential concentration inequality for special U-statistics of order 2, that can be seen as chaos.

Domaines: Statistiques [math.ST]; Probabilités [math.PR]; Théorie [stat.TH]

P Hodara, Patricia Reynaud-Bouret. EXPONENTIAL INEQUALITY FOR CHAOS BASED ON SAMPLING WITHOUT REPLACEMENT. Statistics and Probability Letters, 2019, 146. ⟨hal-01861340⟩