Finite Sample Inference for Targeted Learning

Understand

The Highly-Adaptive-Lasso(HAL)-TMLE is an efficient estimator of a pathwise differentiable parameter in a statistical model that at minimal (and possibly only) assumes that the sectional variation norm of the true nuisance parameters are finite.

• It relies on an initial estimator (HAL-MLE) of the nuisance parameters by minimizing the empirical risk over the parameter space under the constraint that sectional variation norm is bounded by a constant, where this constant can be selected with cross-validation.
• In the formulation of the HALMLE this sectional variation norm corresponds with the sum of absolute value of coefficients for an indicator basis.
• Due to its reliance on machine learning, statistical inference for the TMLE has been based on its normal limit distribution, thereby potentially ignoring a large second order remainder in finite samples.