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Hypothesis tests with precedence probabilities and precedence‐type tests

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Precedence probabilities are important tools in a statistician's toolkit. Precedence probabilities can be defined as the probability of observing single samples from K populations in a particular order. Noting that there are K ! possible orders of K populations; these K ! parameters are a useful way to measure the effectiveness of a classifier (AUC/VUS/HUM). Receiver operating characteristic (ROC) curve/surface/manifold, which can be generated by any classifier leads to calculation of the area under curve (AUC)/volume under surface (VUS)/hyper‐volume under manifold (HUM) can be approximated by a single precedence probability and can be nonparametrically estimated via rank‐based U‐statistic. Precedence probabilities can also be used to test equality of K > 2 distribution functions. Hypothesis tests related to both these problems mentioned above are discussed. On the other hand, when we are interested in testing if the K distributions are stochastically ordered, we perform a precedence‐type test. Different nonparametric tests are also discussed in relation to precedence‐type tests.

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Computational Intensive Statistical Methods > Nonparametric Estimation
Statistical Methods > Nonparametric Statistics
Machine Learning > Statistical Methodology

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