Estimation

A cross-fit Riesz representer \(\hat\alpha\) is the input to one-step, DML, and TMLE estimators of the estimand \(\psi\). Pair it with a cross-fit outcome regression \(\hat\mu\) and the influence function gives a \(\sqrt n\)-consistent, asymptotically normal estimator with a Wald CI.

Two routes are documented here:

• Custom code. Write the influence-function arithmetic by hand. ~30 lines for one-step / DML, ~10 more for the TMLE targeting step. No extra dependencies; the math is fully transparent. Walks through the Lalonde NSW dataset in Python and R.

• External packages. Plug rieszreg’s cross-fit \(\hat\alpha\) into DoubleML (Python and R), or use it as a drop-in replacement for the Riesz step inside EconML’s automatic_debiased_ml. R users on tlverse can pass \(\hat\alpha\) as a learned nuisance into tmle3.

Cross-fitting itself happens at the rieszreg boundary via sklearn.model_selection.cross_val_predict — see Tuning and cross-fitting. What’s downstream of that is what these two pages cover.