We introduce a simple new hypothesis testing procedure, which, based on an independent sample drawn from a certain density, detects which of k nominal densities is the true density is closest to, under the total variation (L 1 ) distance. We obtain a density-free uniform exponential bound for the probability of false detection. Key words and phrases: robust detection, hypotheses testing School of Computer Sciences, McGill University, Montreal, Canada H3A 2K6. e-mail: firstname.lastname@example.org y Dept. of Computer Science and Information Theory, Technical University of Budapest, 1521 Stoczek u. 2, Budapest, Hungary. e-mail: email@example.com z Department of Economics, Pompeu Fabra University, Ramon Trias Fargas 25-27, 08005 Barcelona, Spain. e-mail: firstname.lastname@example.org 1 1 Result A model of robust detection may be formulated as follows: let f (1) ; : : : ; f (k) be xed densities on R d which are the nominal densities under k hypotheses. We observe i.i.d. random vectors X 1 ; : : :..