ABSTRACT
The growth of machine learning as a field has been accelerating with increasing interest and publications across fields, including statistics, but predominantly in computer science. In this chapter, the authors argue that, in order to preserve statistical inference, they should preference sieve maximum likelihood estimators (MLEs) as much as possible. It has been established that the nonparametric bootstrap consistently estimates the multivariate normal limit distribution of the plug-in HAL-MLE for a vector of target features. In recent work, higher-order TMLEs were proposed that target extra score equations beyond the first-order canonical gradient of the target feature, which are selected so that the exact second-order remainder for the plug-in TMLE will become a higher-order difference. Sieve MLEs solve score equations and, thereby, are able to approximately solve a class of score equations – possibly enough to approximate efficient influence curves of the target features of interest, and thus be asymptotically efficient for these target features.
