title: Any discrimination rule can have an arbitrarily bad probability of error for finite sample size.
abstract: Consider the basic discrimination problem based on a sample of size n drawn from the distribution of (X, Y) on the Borel sets of Rdx {O, 1}. If 0 < R*< is a given number, and 'n - 0 is an arbitrary positive sequence, then for any discrimination rule one can find a distribution for (X, Y), not depending upon n, with Bayes probability of error R* such that the probability of error (Rn) of the discrimination rule is larger than R* + 'On for infinitely many n. We give a formal proof of this result, which is a generalization of a result by Cover [1].
authors.affiliation: School of Computer Science, McGill University, Montreal, P.Q., Canada.
authors.forename: L
authors.initials: L
authors.lastname: Devroye