I find it much more believable that I could estimate both nuisances consistently, but at slower rates, vs that I could pick 2 parametric models (without looking at data) & happen to get one exactly correct
Comments
Log in with your Bluesky account to leave a comment
My thoughts aren't fully formed but it's something I have been thinking about. I wonder whether everything has to be 'exactly correct'. It seems like 'close enough' projections get us 'close' to the function? At least for the decimal places we report. So does it matter if it isn't exact?
The m-estimator logic certainly relies on “exactly correct”
Once you start moving to “close enough” to me that means you’re no longer getting precise root-n rates with the nuisances. Then you’ll have to deal with the bias/variance consequences just as if you were using flexible ML
If we really rely on 2 parametric models, we should of course use a variance estimator recognizing this. But this is more about how we model nuisances vs DR estimator itself
Also our paper here suggests strictly more assumptions are needed for DR inference vs estimation:
Comments
Once you start moving to “close enough” to me that means you’re no longer getting precise root-n rates with the nuisances. Then you’ll have to deal with the bias/variance consequences just as if you were using flexible ML
Also our paper here suggests strictly more assumptions are needed for DR inference vs estimation:
https://arxiv.org/pdf/2305.04116
https://arxiv.org/pdf/2405.08525
I think DR estimation vs inference are two quite different things and we need different assumptions to make them work