Any Discrimination Rule Can Have an Arbitrarily Bad Probability of Error for Finite Sample Size

Authors:
Luc Devroye
Affiliations:
School of Computer Science, McGill University, Montreal, P.Q., Canada.
Venue:
IEEE Transactions on Pattern Analysis and Machine Intelligence
Year:
1982

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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