Cramér–Rao bound
The Cramér–Rao bound is a way of measuring how good an estimate of something is. It tells us how much better or worse our estimate might be from the true value. To understand it, let’s look at an example.
Suppose you are trying to estimate the weight of an orange. You can weigh it on a scale, but it’s hard to get the exact weight since the scale isn’t very precise. So you weigh the orange several times, and you get different numbers each time. Those numbers represent your estimates of the orange’s weight.
The Cramer-Rao Bound tells us how close each of these estimates are to the true value of the orange’s weight. It tells us how close our best estimate is, and how much uncertainty there is in the estimates. In other words, it shows us how accurate our estimates are.
Suppose you are trying to estimate the weight of an orange. You can weigh it on a scale, but it’s hard to get the exact weight since the scale isn’t very precise. So you weigh the orange several times, and you get different numbers each time. Those numbers represent your estimates of the orange’s weight.
The Cramer-Rao Bound tells us how close each of these estimates are to the true value of the orange’s weight. It tells us how close our best estimate is, and how much uncertainty there is in the estimates. In other words, it shows us how accurate our estimates are.