Nonparametric detection using empirical distributions and bootstrapping

This paper addresses the problem of decision making when there is no or very vague knowledge about the probability models associated with the hypotheses. Such scenarios occur for example in Internet of Things (IoT), environmental surveillance and data analytics. The probability models are learned from the data by empirical distributions that provide an accurate approximation of the true model. Hence, the approach is fully nonparametric. The bootstrap method is employed to approximate the distribution of the decision statistic. The actual test is based on the Anderson-Darling test that is shown to perform reliably even if the empirical distributions differ only slightly. The proposed detector allows controlling Type I and II error levels without specifying explicit probability models or performing tedious large sample analysis. It is also proved that the test can achieve the specified power. Numerical simulations validate the results.