Please have some patience with me -- I managed to get a B.S. in Math without covering any formal statistics:

The MLE I give is an estimator of the Rayleigh parameter

*sigma*. I assume the source of the bias is analogous to the bias in standard deviation estimators resulting from the presence of an exponent in the sample sum. (In fact,

the Rayleigh distribution has relationships to other common distributions, so I am hoping no new ground needs to be broken to answer my question!)

Checking MOM: The distribution only has one parameter, so MOM only has us looking at the first moment, [TEX]m_1 = \sigma \sqrt{\frac{\pi}{2}}[\TEX], or [TEX]\sigma = m_1 \sqrt{\frac{2}{\pi}}[\TEX]: a constant times the sample mean, which I guess tells us once again that the bias is a result of the concavity of the $\displaystyle \sqrt{n}$ in the estimator for sigma. Have I used MOM correctly?

Again, given the similarities, I wouldn't be surprised to see $\displaystyle c_4$ show up here, but I can't make the connection.

P.S. Any hints on why the two Latex expressions in the third paragraph aren't rendering?