In pursuit of automated statistical inference under minimal assumptions using machine learning tools

Abstract

This dissertation consists of three projects aiming for automated statistical inference under minimal assumptions using machine learning tools. In the first project, we developed two sieve-like methods to construct asymptotically efficient plug-in estimators under nonparametric models. Compared to existing methods, they require less expertise in semiparametric efficiency theory in implementation or rely on weaker smoothness assumptions than traditional sieve estimation and kernel-based methods. In the second project, we studied estimation and evaluation of optimal individualized intervention rules under treatment resource constraints with an instrumental variable (IV). We separately consider intervention on the treatment and the causal IV. We proposed to utilize machine learning tools to estimate optimal rules and efficient plug-in estimators of average causal effects of optimal rules under locally nonparametric models. In the third project, we studied estimation under rich (potentially locally nonparametric) models while utilizing prior information. We proposed to use Gamma-minimax estimators, which minimizes the worst-case Bayes risk over a set of prior distributions that are consistent with prior information. We also proposed to use neural networks to parameterize the class of candidate estimators and developed algorithms to compute an approximate Gamma-minimax estimator with theoretical convergence guarantees.