Mode identification with finite statistics (Corresp.)

The multiple decision problem of identifying the mode of a discrete (
k
-valued) random variable is examined under a time-varying finite memory constraint. Under the assumption that the distribution of the observed random variable has a unique mode, the partial information model, in which it is assumed that the two largest probabilities can be separated by a known number, is shown to be
2k
state perfectly achievable. The general model, in which no assumptions are made on the distribution save the fact that the mode is unique, is shown to be
4k (k - 1)
state perfectly achievable.