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Consider a decision problem aimed at minimizing the expected loss1 where the argument is a parameter estimate. In a Bayesian setting, given a posterior distribution of the parameter and the loss function, one can obtain (analytically or numerically) a point estimate that minimizes the expected loss.

What about the frequentist setting? A posterior is not available. Would it make sense to substitute the posterior with the confidence/fiducial distribution? Or should one do something else?

1The same problem could be easily reformulated as maximization of expected utility instead of minimization of expected loss.

Richard Hardy
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  • You compare the risk curves rather than averaging over them to compare two numbers. There are many ways to compare curves, leading to quite a few different approaches. A good way to learn this would be to consult a classic textbook. – whuber Feb 25 '20 at 15:56
  • @whuber, thank you. I am aware of textbooks on Bayesian decision theory, but here I am dealing with the frequentist case. What kind of textbook contains the relevant information? What are some keywords to look for within the textbook? – Richard Hardy Feb 25 '20 at 16:17
  • I'm referring specifically to frequentist texts. My favorite is J. C. Kiefer, *Introduction to Statistical Inference* (Springer). He writes from the frequentist decision-theoretic standpoint but respects Bayesian approaches, discusses them, and includes them in the book and its many exercises. Some keywords include "admissibility," "minimax," and "risk function." – whuber Feb 25 '20 at 16:23
  • @whuber, this is helpful, thank you! I am loving the first chapters already. I met Nicolas Kiefer at Cornell a few times, might he be a relative of J.C.Kiefer? – Richard Hardy Feb 25 '20 at 17:07

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