## Efficient Estimators and CRLB

It has been reiterated that not all estimators are efficient. Even not all the MVUE are efficient. Then how do we quantify whether the estimator designed by us is efficient or not? An efficient estimator is defined as the one that is * Unbiased (Mean of the estimate = true…

## Applying Cramer Rao Lower Bound (CRLB) to find a Minimum Variance Unbiased Estimator (MVUE)

It was mentioned in one of the earlier articles that CRLB may provide a way to find a MVUE (Minimum Variance Unbiased Estimators). Theorem: There exists an unbiased estimator that attains CRLB if and only if, Here $$ln \; L(\mathbf{x};\theta)$$ is the log likelihood function of x parameterized…

## Cramer Rao Lower Bound for Scalar Parameter Estimation

Consider a set of observed data samples $$X={X_1,X_2,X_3,\cdots X_N}$$ and $$\theta$$ is the scalar parameter that is to be estimated from the observed samples. The accuracy of the estimate depends on how well the observed data is influenced by the parameter $$\theta$$. The observed…
As discussed in the introduction to estimation theory, the goal of an estimation algorithm is to give an estimate of random variable(s) that is unbiased and has minimum variance. This criteria is reproduced here for reference $$E\left\{\hat{f}_0 \right\} = f_0$$ $$\sigma^{2}_{\hat{f}_0}=E\left\{(\hat{f}_0 – E)^2 \right\}$$ In the…