Minor inconsistency between user guide notation and the code?

[doubleml]

Minor inconsistency between user guide notation and the code?

[MalteKurz]

Hi @brgordon1,

thanks for your remark. Let me try to clarify this: In the field obj_dml$se you find the asymptotic standard error, i.e.,
.
It is the standard error from the asymptotic normal distribution scaled with the square-root of the number of observations. We know that

with

If you now for example want to construct a confidence interval for your parameter estimate, you get the following expression

So the asymptotic variance of your parameter estimate is
and the standard error that we return in obj_dml$se is the square-root of it.
In the referenced code line, we compute the asymptotic variance (i.e., before taking the square-root but already with the additional scaling with N):

doubleml-for-r/R/double_ml.R

Line 1231 in d2f108e

sigma2_hat = 1 / n_obs * mean(psi^2) / (J^2)

I hope this helps you. We btw also mention this for example here https://docs.doubleml.org/stable/guide/se_confint.html (see screenshot).

However, I fully agree that this could be made clearer at some places in the documentation, e.g., the API doc here: https://docs.doubleml.org/r/stable/reference/DoubleML.html#public-fields.

Thanks,
Malte

[brgordon1]

Thank you, @MalteKurz. Very helpful and I appreciate the quick reply. I should really have caught that myself by looking at the expression for the confidence interval. I'm glad it now makes sense.

Regards,
Brett

[MalteKurz]

No worries, thanks for the feedback 👍. I think your point was valid and we could make the documentation clearer in this regard.