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Limit theorems for U-statistics indexed by a one dimensional random walk

Nadine Guillotin-PlantardVéronique Ladret — 2005

ESAIM: Probability and Statistics

Let ( S n ) n 0 be a -random walk and ( ξ x ) x be a sequence of independent and identically distributed -valued random variables, independent of the random walk. Let h be a measurable, symmetric function defined on 2 with values in . We study the weak convergence of the sequence 𝒰 n , n , with values in D [ 0 , 1 ] the set of right continuous real-valued functions with left limits, defined by i , j = 0 [ n t ] h ( ξ S i , ξ S j ) , t [ 0 , 1 ] . Statistical applications are presented, in particular we prove a strong law of large numbers for U -statistics...

Limit theorems for U-statistics indexed by a one dimensional random walk

Nadine Guillotin-PlantardVéronique Ladret — 2010

ESAIM: Probability and Statistics

Let ( be a -random walk and ( ξ x ) x be a sequence of independent and identically distributed -valued random variables, independent of the random walk. Let be a measurable, symmetric function defined on 2 with values in . We study the weak convergence of the sequence 𝒰 n , n , with values in the set of right continuous real-valued functions with left limits, defined by i , j = 0 [ n t ] h ( ξ S i , ξ S j ) , t [ 0 , 1 ] . Statistical applications are presented, in particular we prove a strong law of large numbers for -statistics indexed by a one-dimensional...

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