A simple class of asymptotically optimal quantizers

Abstract

A simple class of quantizers is introduced which are asymptotically optimal, as the number of quantization levels increases to infinity, with respect to a mean <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</tex> th power absolute error distortion measure. These asymptotically optimal quantizers are very easy to compute. Their performance is evaluated for several distributions and compares favorably with the performance of the optimal quantizers in all cases for which the latter have been computed. In addition their asymptotic robustness is studied under location, scale, and shape mismatch for several families of distributions.