Targeted learning: From MLE to TMLE

• Published in: Past, Present, and Future of Statistical Science pp. 489 - 504
• Format: Book Chapter
• Language: English
• Published: Chapman and Hall/CRC 2014
• Subjects: True Q0; Van Der Laan; MNP; Semi-parametric Models; Candidate Estimators; Observed Data Distribution; Influence Curve; Minimax Rate; Statistical Inference; Oracle Results; Donsker Classes; Fine Tuning Parameter; Score Equation; Failure Time Data; Kaplan Meier Estimator; Parametric MLE; Statistical Estimation Problem; Adaptive Estimators; NPMLE; Bivariate Survival Function; Asymptotic Linearity; Van Der Vaart; Bivariate Failure Time; Functional Delta Method; Substitution Estimators
• DOI: 10.1201/b16720-47

In this chapter I describe some of the essential elements of my past scientific journey from the study of nonparametric maximum likelihood estimation (NPMLE) to the field targeted learning and the resulting new general tool targeted minimum loss based estimation (TMLE). In addition, I discuss our current and future research program involving the further development of targeted learning to deal with dependent data. This journey involved mastering difficult statistical concepts and ideas, and combining them into an evolving roadmap for targeted learning from data under realistic model assumptions. I hope to convey the message that this is a highly inspiring evolving unifying and interdisciplinary project that needs input for many future generations to come, and one that promises to deal with the current and future challenges of statistical inference with respect to a well-defined typically complex targeted estimand based on extremely highly dimensional data structures per unit, complex dependencies between the units, and very large sample sizes.