CV-TMLE for Nonpathwise Differentiable Target Parameters
TMLE has been developed for the construction of efficient substitution estimators of pathwise differentiable target parameters. Many parameters are nonpathwise differentiable such as a density or regression curves at a single point in a nonparametric model. In these cases one often uses a specific estimator under a specific smoothness assumptions for which it is possible to establish a limit distribution and thereby provide statistical inference. However, such estimators do not adapt to the true unknown smoothness of the data density and, as a consequence, can be easily outperformed by an adaptive estimator that is able to adapt to the underlying true smoothness.
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