A unified approach to parameter estimation

This paper considers parameter estimation under arbitrary statistical environment. Based on an input quantization, the necessary statistical modeling is simplified to just a measurement of some frequencies of occurrence. 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 G-estimator which consists of an array of identical LOE's is presented. In performance analysis, the estimation of the location parameter of a continuous, unimodel, and symmetric distribution is studied. In this case, it is proved that the G-estimator extends the optimality of a single LOE to the large parameter space.