Augmenting an omnibus test with conditionally calibrated secondary statistics and a small Type I error budget preserves primary power and sharply increases sensitivity to feature-specific departures.
Power Studies For Two-Sample and Goodness-of-Fit Methods For Multivariate Data
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abstract
We present the results of a large number of simulation studies regarding the power of various goodness-of-fit as well as non-parametric two-sample tests for multivariate data. In two dimensions this includes both continuous and discrete data, in higher dimensions continuous data only. In general no single method can be relied upon to provide good power, any one method may be quite good for some combination of null hypothesis and alternative and may fail badly for another. Based on the results of these studies we propose a fairly small number of methods chosen such that for any of the case studies included here at least one of the methods has good power. The studies were carried out using the R packages MD2sample and MDgof, available from CRAN.
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Priority-preserving augmentation of goodness-of-fit tests by conditional calibration
Augmenting an omnibus test with conditionally calibrated secondary statistics and a small Type I error budget preserves primary power and sharply increases sensitivity to feature-specific departures.