But your estimate isn't very meaningful if you only have enough samples such that the N v (N-1) normalization matters, the variances on the estimator will be to

But your estimate isn't very meaningful if you only have enough samples such that the N v (N-1) normalization matters, the variances on the estimator will be too large. The 1/N normalization comes from the MLE BTW, I'm sure most know this already. As an aside, to see the power of a biased estimator look at the James-Stein Estimator [1]. [1] https://en.wikipedia.org/wiki/James%E2%80%93Stein_estimator https://en.wikipedia.org/wiki/James%E2%80%93Stein_estimator