In this lesson, we’ll overview the concept of the Cramer Rao lower bound for the MSE for the estimation of a deterministic, but unknown parameter, and we show how to compute and interpret this bound for a few simple examples.
@@timothyschulz9853 can you explain how? I have considered zero mean as mentioned in the example. So E[X]=0 and according to the solution, E[X^2]= σ^2. So, using these, I get a positive sign instead of a negative.
For an unbiased estimator E[σ']=σ, where σ' is sigma hat. So, E[(σ'-σ)^2] = E[σ'^2 + σ^2 -2σ*σ'] = (π/2)E[X^2] + E[σ^2] - 2σE[σ'] = (π/2)σ^2 + σ^2 - 2σ^2 = your solution. However, if I consider E[σ'] = sqrt(π/2)*E[X], this term goes to 0 as E[X]=0. Can you please explain as to why the second approach is incorrect?
