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!Efficiency(https://stackoverflow.com/20240427_193105.jpg). Given snapshot of the book states that among the class of consistent estimators, in general, more than one consistent estimator of a parameter exists. Then it lay down the requirement for choosing the estimators among the class of consistent estimators based on their sampling variance. The definition of Most Efficient Estimator is also defined among the class of consistent estimators only. !MVUE(https://stackoverflow.com/20240427_193114.jpg). This snapshot gives the definition of MVUE which is the estimator among the class of unbiased ones and having least variance among them. While I am OK with the definition of the MVUE, I am unable to comprehend about consistency and efficiency. Are efficient estimators to be looked only from the class of consistent estimators only? Many explanations regarding efficiency and efficient estimators link it to the unbiasedness and Cramer-Rao lower bound. What is the inter-relations between them?

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    $\begingroup$ There are many posts available here relevant to these concepts. Have you checked any? $\endgroup$
    – User1865345
    Commented Apr 27 at 14:53
  • $\begingroup$ Also the image links are broken. $\endgroup$
    – User1865345
    Commented Apr 27 at 14:53
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    $\begingroup$ Links broken. Efficiency defined. MVUE defined. $\endgroup$
    – Carl
    Commented Apr 28 at 1:22

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