K-2 rotated goodness-of-fit for multivariate data
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Consider a set of multivariate distributions, F_1,…,F_M, aiming to explain the same phenomenon. For instance, each F_m may correspond to a different candidate background model for calibration data, or to one of many possible signal models we aim to validate on experimental data. In this article, we show that tests for a wide class of apparently different models F_m can be mapped into a single test for a reference distribution Q. As a result, valid inference for each F_m can be obtained by simulating only the distribution of the test statistic under Q. Furthermore, Q can be chosen conveniently simple to substantially reduce the computational time.
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