Doubts about structural equation of DML

[pkwangwanjun]

Hi, I have some doubts about structural equation of DML.

In EconML , structural equation of DML like this :

But in the Robinsons or Chernozhukov paper, structural equation of DML like this :

Are the two equivalent?

By the way , I found another implementation of DML (https://docs.doubleml.org/stable/guide/algorithms.html#algorithm-dml1)

Their algorithm for estimating ATE is as follows :

Can you explain the difference between them and you, I hope to get your reply as soon as possible, thank you .

[kbattocchi]

The partial linear regression specification is basically the same, except that they are not estimating a heterogeneous effect and the variable names differ: their D is our T, their X is our W, and they do not have anything corresponding to our X.

The DML procedure is basically what is implemented in our OrthoLearner base class, what we call DML is specialized to the linear regression case.

[pkwangwanjun]

The partial linear regression specification is basically the same, except that they are not estimating a heterogeneous effect and the variable names differ: their D is our T, their X is our W, and they do not have anything corresponding to our X.

The DML procedure is basically what is implemented in our OrthoLearner base class, what we call DML is specialized to the linear regression case.

Hi, but I found that their assumptions are different, does this have no effect?