Abstract:
We review targeted maximum likelihood estimation (TMLE), which provides a general template for the construction of asymptotically efficient plug-in estimators of a differentiable target parameter. TMLE involves maximizing a parametric likelihood along a so-called least favorable parametric model through an initial estimator of the data density, and iterating this updating process till convergence. For one-dimensional target parameters, we propose a universal least-favorable submodel that (a) guarantees that the TMLE only takes one step, and thus always exists in closed form, and (b) renders the targeting step of the TMLE maximally effective, resulting in meaningful practical improvements relative to an iterative TMLE. We generalize this to multivariate and infinite-dimensional parameters, and illustrate our proposal in several causal estimation problems. The asymptotic efficiency of the TMLE relies on the asymptotic negligibility of a second-order term. This typically requires the initial data density estimator to converge fast enough. We propose a new estimator, the Highly Adaptive LASSO (HAL), of the data density (and its functionals) that converges at a sufficient rate regardless of the dimensionality of the problem, under almost no additional regularity. This allows us to propose a one-step TMLE that is asymptotically efficient in great generality across all models and differentiable target parameters. We demonstrate the practical performance of HAL and its corresponding TMLE for the average causal effect.