# Biased and Efficient estimators

Is unbiasedness a necessary condition for an estimator to be efficient?

For example, if $\hat {\theta}= \frac{\sum_i^n X_i}{3}$, I assume $\hat {\theta}$ can't be efficient in a Cramer-Rao lower bound context because $E[\hat {\theta}]= \frac {\theta}{3}$.

A possible way to compare two estimators is to use Mean Squared Error : \begin{align*} MSE = Bias^2 + Variance \end{align*}.