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A general and relatively simple method for construction of multivariategoodness-of-fit tests is introduced. The proposed test is applied to ellipticaldistributions. The method is based on a characterization of probabilitydistributions via their characteristic function. The consistency and otherlimit properties of the new test statistics are studied. Also in a simulationstudy the proposed tests are compared with earlier as well as more recentcompetitors.

A general Monte Carlo method for multivariate goodness-of-fit testing applied to elliptical families