|
Abstract:
|
We review targeted minimum loss estimation (TMLE), which provides a general template for the construction of asymptotically efficient plug-in estimators of a target estimand for infinite dimensional models. TMLE involves maximizing a parametric likelihood along a so-called least favorable parametric model through an initial estimator (e.g., ensemble super-learner) of the relevant functional of the data distribution. The asymptotic normality and efficiency of the TMLE relies on the asymptotic negligibility of a second-order term. This typically requires the initial estimator to converge at a rate faster than n-1/4. We propose a new estimator, the Highly Adaptive LASSO (HAL), of the data distribution and its functionals that converges at a sufficient rate regardless of the dimensionality of the data/model, under almost no additional regularity. This allows us to propose a general TMLE that is asymptotically efficient in great generality. We demonstrate the practical performance of HAL and its corresponding TMLE for the average causal effect for dimensions up till 10. We also discuss a nonparametric bootstrap method for inference taking into account the higher order contributions of
|
