EXTREMAL PROPERTIES OF LIKELIHOOD-RATIO QUANTIZERS

Let there be M hypotheses H-1,..,H(M), and let Y be a random variable, taking values in a set Y, with a different probability distribution u nder each hypothesis. A quantizer gamma : Y bar arrow pointing right { 1,...,D} is applied to form a quantized random variable gamma(Y). We c haracterize the extreme points of the set of possible probability dist ributions of gamma(Y), as gamma ranges over all quantizers. We then es tablish optimality properties of likelihood-ratio quantizers for a ver y broad class of quantization problems, including problems involving t he maximization of an Ali-Silvey distance measure and the Neyman-Pears on variant of the decentralized detection problem.