Deviation detection with continuous observations

This paper considers the detection of possible deviation from a nominal distribution for continuously valued random variables. Specifically, under the null hypothesis, samples are distributed approximately according to a nominal distribution. Any significant departure from this nominal distribution constitutes the alternative hypothesis. It is established that for such deviation detection where the nominal distribution is only specified under the null hypothesis, Kullback-Leibler distance is not a suitable measure for deviation. Subsequently, Lévy metric is adopted and an asymptotically δ-optimal detector is identified for this problem.