Interview Question: Best Estimators

Sample Question #164 (statistics)

Are unbiased estimators always the best estimators of a model? If so, can you prove it? If not, can you provide a counter-example?

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One Response to Interview Question: Best Estimators

  1. Brett says:

    ANSWER
     
    First, we need to define what "best" means. An estimator is "best" when it is consistent (i.e., tends to the true parameter value in large samples) and efficient (i.e,. has the lowest "loss" with regard to some loss function among all estimators — usually, but not always, the loss function is taken to be the estimator’s variance).  Unbiasedness (which means the estimator having expectation equal to the true parameter value) is often not the most desirable feature.  An example is the James-Stein shrinkage estimator which is biased but has a quadratic loss less than the unbiased estimator (namely, the sample mean).  There’re also examples of unbiased estimators that have very large variances which are undesirable because they give us low confidence in point estimates generated by the estimator.
     

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