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> Unbiasedness of the decision procedure means that γ is indeed the function it estimates the best, and it is not a better estimator for any other function γ'(θ
by 6gvONxR4sf7o 6y ago
> Unbiasedness of the decision procedure means that γ is indeed the function it estimates the best, and it is not a better estimator for any other function γ'(θ).
Are you suggesting that unbiased estimators are necessarily better than biased ones? If so, check out Stein’s phenomenon for a counterexample. It’s common for biased estimators to dominate unbiased ones in terms of error rates. That’s where the bias variance trade off in ML comes from.
https://en.wikipedia.org/wiki/Stein's_example https://en.wikipedia.org/wiki/Stein's_example
- yccs27 6y agoIndeed, the unbiasedness condition for an estimator says nothing about its quality relative to other estimators. Instead, it requires that you cannot change the target function γ without the expected loss becoming worse. The paper I referenced even includes a theorem saying that, as long as the value to be estimated can not be exactly deduced from the observation, no estimator is both Bayes-optimal and unbiased. However for many observations, the Bayes-optimal estimator becomes asymptotically unbiased.