On the Problem of Bias in Multinomial Classification

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Abstract
Assuming sampling from 2 multinomial distributions and the use of a sample based likelihood ratio rule as an optimal classification procedure, an algebraic expression is derived for the exact bias of the apparent error rate. Properties that govern the behavior of the bias are discussed and comparisons to a bound by Glick are made. Tables are generated giving exact state bias for various combinations of state probabilities and sample sizes. Suggestions are provided for proceeding in practical situations.

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