Issue No. 02 - February (1982 vol. 4)

ISSN: 0162-8828

pp: 154-157

Luc Devroye , School of Computer Science, McGill University, Montreal, P.Q., Canada.

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].

INDEX TERMS

CITATION

Luc Devroye, "Any Discrimination Rule Can Have an Arbitrarily Bad Probability of Error for Finite Sample Size",

*IEEE Transactions on Pattern Analysis & Machine Intelligence*, vol. 4, no. , pp. 154-157, February 1982, doi:10.1109/TPAMI.1982.4767222