I am self learning estimation theory and finding it quite difficult to grasp the utility of Cramer Rao Lower bound. In text books and online tutorials always say that one should derive the CRLB of the estimator. If the variance of the estimator is greater than equal to the inverse of the Fisher information, then we say that no other better estimator exists. The inverse of the Fisher information is the CRLB. If the variance is equal to the CRLB, then the estimator is efficient. Intuitively, an estimator is nothing but a formula or an expression that is used to find an unknown value/ parameter.
1) Is there a better intuitive way to explain what CRLB bound tells us and why we need it?
2) What is meant by efficient estimator and efficiency to do what? With what do we compare the efficiency of an estimator. These questions may be trivial but I found very difficult to extract key information from highly mathematical heavy stuff.
3) Do we discard the estimator if inefficient?
Please correct me if any information is wrong. Thank you.