The Cramer-Rao Inequality

The Cramér-Rao inequality provides a lower bound on how accurately we can estimate an unknown parameter from data. It states that there’s a limit to the precision of any unbiased estimator—meaning, no matter what method we use, we can’t expect to do better than this bound. Essentially, it tells us the best possible accuracy achievable based on the information in the data. This helps statisticians understand the limitations of their estimates and evaluate how efficient an estimator is relative to the optimal possible precision.