Nonparametric estimation algorithms based on input quantization (Corresp.)

The estimation of a parameter of a white discrete-time process with arbitrary statistical distribution is considered, using quantized samples. Because of the quantization the necessary statistical modeling is simplified to the measurement of a few parameters. Under the assumption that the parameter space is a small interval, a locally optimum estimator (LOE) is derived. It is shown that this estimator has a desirable parallel structure for implementation by simple digital hardware. The idea is then extended to the case of a large parameter space for which a -estimator consisting of an array of identical LOE\´s is presented. To analyze the performance of this scheme, the estimation of the location parameter of a continuous, unimodal, and symmetric distribution is studied. In this case it is proved that the -estimator extends the optimality of a single LOE to the larger parameter space.