Displaying similar documents to “A strong invariance principle for negatively associated random fields”

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

Nadine Guillotin-Plantard, Véronique Ladret (2005)

ESAIM: Probability and Statistics

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Let ( S n ) n ≥ 0 be a ℤ -random walk and ( ξ x ) x ∈ ℤ be a sequence of independent and identically distributed ℝ -valued random variables, independent of the random walk. Let h be a measurable, symmetric function defined on ℝ 2 with values in ℝ . We study the weak convergence of the sequence 𝒰 n , 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...

Central limit theorem for sampled sums of dependent random variables

Nadine Guillotin-Plantard, Clémentine Prieur (2010)

ESAIM: Probability and Statistics

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We prove a central limit theorem for linear triangular arrays under weak dependence conditions. Our result is then applied to dependent random variables sampled by a ℤ -valued transient random walk. This extends the results obtained by [N. Guillotin-Plantard and D. Schneider, (2003) 477–497]. An application to parametric estimation by random sampling is also provided.