Papers › A new class of binning free, multivariate goodness-of-fit tests: the energy tests
A new class of binning free, multivariate goodness-of-fit tests: the energy tests
B. Aslan, G. Zech
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We present a new class of multivariate binning-free and nonparametric goodness-of-fit tests. The test quantity \emph{energy} is a function of the distances of observed and simulated observations in the variate space. The simulation follows the probability distribution function f₀ of the null hypothesis. The distances are weighted with a weighting function which can be adjusted to the variations of f₀. We have investigated the power of the test for a uniform and a Gaussian distribution of one or two variates, respectively and compared it to that of conventional tests. The energy test with a Gaussian weighting function is closely related to the Pearson χ² test but is more powerful in most applications and avoids arbitrary bin boundaries. The test is especially powerful in the multivariate case.
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