LAUSR

Abstract The problem under study is detecting the presence, and identifying the exact position, of a block C n of “anomalous” observations in a finite sequence of independent random variables X 1 , … , X n . By “anomalous” we mean that the distribution G of the observations in the block C n is possibly different from the “under control” distribution F of the remaining X i ’s. We first propose a nonparametric approach, based on classical goodness of fit (Kolmogorov–Smirnov (KS) and Cramer–von Mises (CvM)) statistics, for the case of real random variables X i . An application in stochastic geometry is outlined. Lastly, we focus on the case where the X i are functional data, that is, trajectories of a stochastic process X = X ( t ) , t ∈ [ 0 , 1 ] . The strategy we follow in this case is to take the functional data to the real line with an appropriate transformation and then using the nonparametric detection/identification methodologies mentioned above. The real valued transformation we propose is the Radon–Nikodym derivative of the “under control” distribution (that assumed for most observations) with respect to another suitably chosen reference distribution.