Robust Sequential Probability Ratio Detectors.

摘要

A statistical hypothesis test is developed for situations in which uncertainty exists in the underlying probability distributions of the observations. The resulting test, called the robust sequential probability ratio test (RSPRT), provides a theoretical framework within which specific detection problems can be formulated. As the name implies, the RSPRT is sequential in nature, and it guarantees a given performance level (in terms of error probabilities). Application of the RSPRT requires the definition of disjoint classes of distributions which contain the distribution of the observations under each respective hypothesis, the determination of 'least favorable' sequences of distributions. The likelihood ratio between these sequences forms the basic structure of the test. The RSPRT is applied to two models of uncertainty which frequently arise in practice. In the first, the distribution of the observations under each hypothesis is known to lie in the neighborhood of some known nominal distribution, but the exact distributional form is unknown. In the second model, the observations have known univariate Gaussian distributions, but compositeness of the hypotheses results because of uncertain correlation between the observations. In each case the performance measures of the test are examined in detail. The RSPRT is shown to be far superior to a fixed sample size robust test in terms of expected observation length.