Targeted Maximum Likelihood Learning

Suppose one observes a sample of independent and identically distributed observations from a particular data generating distribution. Suppose that one is concerned with estimation of a particular pathwise differentiable Euclidean parameter. A substitution estimator evaluating the parameter of a given likelihood based density estimator is typically too biased and might not even converge at the parametric rate: that is, the density estimator was targeted to be a good estimator of the density and might therefore result in a poor estimator of a particular smooth functional of the density. In this article we propose a one step (and, by iteration, k-th step) targeted maximum likelihood density estimator which…

• NI
  National Institutes of Health