Consistency of general bootstrap methods for degenerate U-type and V-type statistics

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Kernel‐based tests for joint independence (2016, background): “The following two theorems are extensions of results due to Leucht and Neumann (2009) that show that U-and V-statistics based on resampled data keep their respective asymptotic distributions.”
Degenerate $$U$$- and $$V$$-statistics under ergodicity: asymptotics, bootstrap and applications in statistics (2013, methodology): “The bootstrap offers a convenient way to circumvent these problems, see Arcones and Giné (1992), Dehling and Mikosch (1994) or Leucht and Neumann (2009) for the i.i.d. case.”
On Testing Independence and Goodness-of-fit in Linear Models (2013, result): “(cid:0) (cid:1) This argument is similar to that in [LN09].”
Degenerate U- and V-statistics under weak dependence : Asymptotic theory and bootstrap consistency (2012, methodology): “We employ Lemma 4.2 of Neumann and Paparoditis [26] to verify convergence of the finite dimensional distributions.”