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A dependent multiplier bootstrap for the sequential empirical copula process under strong mixing Kojadinovic, Ivan


Two key ingredients to carry out inference on the unknown copula of multivariate observations are the empirical copula process and an appropriate resampling scheme to obtain replicates of the latter. Among the existing resampling techniques used for i.i.d. observations, the multiplier bootstrap introduced in the seminal paper of Rémillard and Scaillet (2009) frequently appears to lead to inference procedures with the best finite-sample properties. Bücher and Ruppert (2013) recently proposed an extension of this technique to strictly stationary strongly mixing observations by adapting the tapered muliplier bootstrap of Bühlmann (1993) to the empirical copula process. The main result of the work to be presented is an unconditional and sequential version of the tapered multiplier bootstrap of Bühlmann whose validity requires substantially weaker conditions on the rate of decay of the strong mixing coefficients and slightly less constrained multipliers. The obtained result can also be regarded as a partial extension of the unconditional multiplier central limit theorem to the case of strongly mixing observations. The resulting generalization of the tapered multiplier bootstrap of Bühlmann is then adapted to the sequential empirical copula process thereby allowing to transpose to the strongly mixing setting all of the existing multiplier tests on the unknown copula, including nonparametric tests for change-point detection. Joint work with Axel Bücher.

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