ON THE METHOD OF H. CHERNOFF IN CLASSIFICATORY PROBLEM BETWEEN TWO CATEGORIES WITH SPECIFIED $ 2^k $-th MOMENT ($ k = 0, 1, 2 $)
Akihiro Nishi · Bulletin of Mathematical Statistics · 1979
In this paper we shall seek the upper bound of probabilities (erorr probabilities) of misclassification in the Bayes classification procedures between two categories whose moments of order $ 2^k $ $ (k = 0, 1, 2) $ are assumed to be known, while the distribution of each category may well be continuous or discrete. We shall also give a sufficient condition, which is an improvement of Becher-Chernoff's upper bound. This becomes also a necessary condition in some cases of interest.