I found a mathematical problem which investigated the statistical properties of a MLE. The MLE is biased and asymptotically unbiased and the variance of the MLE tend towards the CRLB at larger sample sizes (calculated on the fact of biased estimators). Does this mean that the MLE is an asymptotically minimum variance unbiased estimator? If so, is there any proofs that need to be done to show this and how?
2026-04-01 04:23:55.1775017435
Can a biased MLE estimator that is asymptotically unbiased be a asymptotically minimum variance estimator if it approaches the CRLB asmptotically?
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