Cramér-Rao bound

The Cramér-Rao bound is a fundamental concept in statistics that sets a limit on how precisely we can estimate an unknown parameter from data. It tells us the lowest possible variance (or uncertainty) any unbiased estimator can achieve, given the data's information content. In other words, it defines the best closest estimate we can hope for, highlighting the inherent limitations posed by the data itself. This helps statisticians understand how well they can expect to estimate a quantity and whether an estimator is close to optimal.