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Guillaume Dehaene
Guillaume Dehaene
10:58
Great lively discussion on my question on randomized tests. I did not expect that ^__^
The community here is super high level: it's awesome!
I agree with your frustration nick, but it's a feature of SE and I doubt they change it.
Given that many questions here are fairly didactic, it doesn't annoy me too much
User1865345
User1865345
11:58
@GuillaumeDehaene have you considered in general the necessity of randomized decision rules?
In estimation theory also, there does exist randomized estimators but when working in convex loss functions, we work with non randomized estimators.
In counterexamples book, Romano gave an illustration where nonrandomized tests at level less than 0.5 have no power. But this is a highly contrived example.
At the end of the day, C&B is way less technical book than the other counterparts available. They have omitted many discussions the presence of which could have been appreciated, but the book was intended for early undergrads.
 
2 hours later…
Guillaume Dehaene
Guillaume Dehaene
13:44
I'm not sure I see your point?
I see the similarity with testing: randomizing enables you to interpolate between two rules and reach a compromise loss between the two.
I'm not really sure I see a great argument in their favor there either (at least for me: with decision rules, it's a bit more natural to say that a deterministic rule can sometimes be bad since it would make you exploitable if that's an issue in that context)? It's a bit more natural to consider randomized rules there, I guess? Still, the tension between:

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