Fast estimation of uniformly-distributed random processes using extreme values

The nonlinear estimation, due to R. A. Fisher, of the mean of a uniformly-distributed random variable given by the average of the extreme values of N samples is unbiased. Furthermore, the variance of the estimation is very much less than that for the conventional linear estimation. Two extreme-based estimation of variance are considered, and their properties investigated for uniform, Gaussian and Laplacian distributions.