Answer:
Since the name indicates Minimum Variance Unbiased Estimator-first of all it is a parameter estimator. Secondly, it is an unbiased estimator so that the sample is carried out randomly. I.e. whenever a sample is chosen, there is no personal bias.
Then we can consider more than one sample-based unbiased estimator but sometimes they can vary in variation. But we have always intended to select an estimator that has minimal variance.
Therefore if the unbiased estimator has minimal variation between all unbiased class estimators then it is known as a good estimator.
The advantage of MVUE is that it is impartial and has a minimal variance of all unbiased estimators amongst the groups.
At times we get an estimator such as MLE which is not unbiased because the sample can be personally biased. Now let us assume an instructor needs to find the lowest marks in a physics class. Presume an instructor picks a sample and interprets the lowest possible marks.
Again the mistake could be that the instructor may choose his favorite sample learners because the sample might not be selected randomly. Therefore it is important to select an unbiased estimate with a minimum variance.
