Multiple objects: error exponents in hypotheses testing and identification
Information Theory, Combinatorics, and Search Theory
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It is pointed out that the basic results can be proved fairly easily if one uses a Sanov theorem for the distribution of types. Such a theorem comes easily from large deviation theory. A caveat is that this technique only identifies the error exponent up to terms o(n) in the exponent, whereas the combinatorial arguments give an estimate up to terms O(log n) in the exponent