Exponential inequalities and functional central limit theorems for random fields

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An empirical central limit theorem for dependent sequences (2007, methodology): “We first recall two moment inequalities given in Dedecker [9].”
Rosenthal-type inequalities for the maximum of partial sums of stationary processes and examples (2011, background): “The inequality (17) follows now by the maximal inequality (6).”
Maximal Inequalities and Empirical Central Limit Theorems (2002, background): “We first recall a central limit theorem for non uniform mixing sequences (cf. Dedecker [7], Corollary 3): Theorem 5.1.”
FIXED-b ASYMPTOTICS FOR SPATIALLY DEPENDENT ROBUST NONPARAMETRIC COVARIANCE MATRIX ESTIMATORS (2014, methodology): “We generate instruments and errors as geometrically decaying spatial moving averages of order 15: zs,h = ∑ ‖ j‖≤15 γ ‖ j‖ws+ j,h for h = 1,2,3, εs = ∑ ‖ j‖≤15 γ ‖ j‖us+ j,1, and vs = ∑ ‖ j‖≤15 γ ‖ j‖us+ j,2, where ‖ j‖ = max( j1, j2); us,1 = .8us,2 + .6es ; and es , us,2, ws,1, ws,2, and ws,3 are…”