### Statistical Analysis of a Quantizer Design Algorithm

#### Abstract

Suppose that a sequence of probability distribution functions [F

_{n}] converges weakly to a distribution function F. Does the sequence of optimal quantizers for the F_{n}’s converge to an optimal quantizer for F? If so, do the respective distortions converge to the optimal distortion for F? It is shown that uniform integrability of the cost function with respect to the sequence {F_{n}} is sufficient to obtain such convergence for mean-square distortion. These questions are used to motivate a study of the strong consistency properties of optimal quantizer designs based on sampled data.