I have a small number of samples from a Rayleigh process, and I am trying to estimate the Rayleigh parameter sigma.
This popular exercise suggests that is an unbiased estimator for sigma. Except that it doesn't come close to the underlying sigma unless you take the square root of the result, and even then it is biased for small n! (I verified this via monte carlo simulation.)
So for small Rayleigh populations is there a BLUE, or a correction term to the MLE ?
Furthermore, what can I say about confidence in the parameter estimate for a given population of n samples?