I have no idea about testing for semi-parametric models, but I’m sure Judith or Chris have definite ones!

]]>I’m not sure how fair your criticism that he appears to only review and expand on his own work is. I’m not sure that there is much else out there. Would that we put as much work into this type of problem as we do into studying the inference for the mean of a normal distribution! (To venture a controversial opinion that isn’t based around colour preference!)

This actually makes me think of an important question that I can’t get my head around: how does hypothesis testing work for these models?

A similar question is “How does hypothesis testing work for a semi-parametric model?”

In both cases, the testing result will be strongly prior dependent (the first case will depend on the restriction of the prior to the identified region, the second will depend on the prior of the scale parameter for the non-parametric effect). So is there a framework for asking these sorts of questions?

As for tying down identifiable vs non-identifiable parts (and actually all of the (iii) question in your second paragraph), I suspect we need to tie up a computationally minded algebraic geometer and tickle them until they give us the answers…

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