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The process comparing the empirical cumulative distribution function of thesample with a parametric estimate of the cumulative distribution function isknown as the empirical process with estimated parameters and has beenextensively employed in the literature for goodness-of-fit testing. Thesimplest way to carry out such goodness-of-fit tests, especially in amultivariate setting, is to use a parametric bootstrap. Although very easy toimplement, the parametric bootstrap can become very computationally expensiveas the sample size, the number of parameters, or the dimension of the dataincrease. An alternative resampling technique based on a fast weightedbootstrap is proposed in this paper, and is studied both theoretically andempirically. The outcome of this work is a generic and computationallyefficient multiplier goodness-of-fit procedure that can be used as alarge-sample alternative to the parametric bootstrap. In order to approximatelydetermine how large the sample size needs to be for the parametric and weightedbootstraps to have roughly equivalent powers, extensive Monte Carlo experimentsare carried out in dimension one, two and three, and for models containing upto nine parameters. The computational gains resulting from the use of theproposed multiplier goodness-of-fit procedure are illustrated on trivariatefinancial data. A by-product of this work is a fast large-samplegoodness-of-fit procedure for the bivariate and trivariate t distribution whosedegrees of freedom are fixed.

Goodness-of-fit testing based on a weighted bootstrap: A fast large-sample alternative to the parametric bootstrap