Optimum quantization of order statistics

We present necessary conditions for minimum mean square error (MMSE) quantization of order statistics. These conditions are obtained by observing that in a quantize-sort cascade system, operations of quantization and sorting are interchangeable. We consider MMSE quantization of a single order statistic as well as of a group of order statistics and highlight several interesting properties. Numerical characteristics of order statistic quantizers are presented for Gaussian and uniform distributions, and detailed comparisons are made