When use Doubly Robust Estimator we train m0/m1 models and propensity score model to be used by the estimator.

Is it OK to use the same dataset to train those models and then use them to measure ATE in this same data? Or should we alway separate Train and Validation subsets of the data to do it correctly?

Please explain why.

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    $\begingroup$ I believe that most of the DR estimators (especially those pre 2018) do not use sample splitting, but if I am remembering this paper well there are advantages including the ability to achieve optimal rates and efficiency with weaker assumptions (arxiv.org/pdf/2004.14497.pdf). This paper also talks about taking inspiration from Newey and Robins (2018) [arxiv.org/pdf/1801.09138.pdf] which may be the first DR sample splitting estimator at least from a strictly causal perspective. $\endgroup$ – Tyrel Stokes Aug 30 at 2:16
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    $\begingroup$ This answer doesn't directly address your question but is a really clear description of doubly robust estimators and sample splitting. $\endgroup$ – Noah Aug 30 at 3:45

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