A randomized most powerful test to detect a cheater's action. Applicaton to identification of listeriosis in Lombardy

This article presents a new randomized non-parametric test based on a sample of independent but not identically distributed variables; this test detects if a cheater replaces one of the distributions of the sample with a convex-dominating one. The presented test is the uniformely most powerful, in the sense that it is the most powerful for any change of the cheater. We show that this test may be applied when we have variables with distribution satisfying the monotone likelihood ratio property and we need to check whether a parameter of a variable has been changed. The application we present concerns the detection of epidemics of listeriosis in Lombardy from 2005 to 2011.