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SSC Statistics QUESTION #1988
Question 1
Among all unbiased estimators of a parameter \(\theta\), the one with the minimum variance is called:
  • A consistent estimator
  • A sufficient estimator
  • The UMVUE (Uniformly Minimum Variance Unbiased Estimator)✔️
  • A maximum likelihood estimator
Correct Answer Explanation
An estimator that is unbiased AND has the smallest variance among all unbiased estimators for every value of \(\theta\) is called the UMVUE. By the Cramér-Rao inequality, no unbiased estimator can have variance below the Cramér-Rao lower bound.