On the Problem of Bias in Multinomial Classification

Abstract

Summary Assuming sampling from two multinomial distributions and the use of a sample based likelihood ratio rule as ani optimiial classification procedure, ani algebraic expression is derived jor the exact bias of'the apparenit error rate. Properties that govern the behavior oJ'the bias are discussed and comparisons to a bound by Glick (1973) are miiade. Tables are genierated givinig exact state bias jor various combinations of state probabilities and samiiple sizes. Suggestions are provided j6or proceeding in practical situations.