Statistical Methods for Problems in Heterogeneous Populations, from Clinical Trials to Latent-Variable Models

Abstract

This dissertation provides methods for analyzing data from heterogeneous populations and addresses the problems of relative efficiency estimation, estimation in Markov-switching vector autoregressive models, and statistical inference in semiparametric finite mixtures. In Chapter 2, we propose a general framework for using external data available at the planning stage of a clinical trial to identify and make statistical inference about the efficiency gain from covariate adjustment to be expected in this future trial. We propose efficient estimators that allow for the incorporation of flexible statistical learning tools and develop statistical inference procedures to accompany the proposed estimators. In Chapter 3, we develop an approximate regularized Expectation-Maximization algorithm for parameter estimation in Markov-switching vector autoregressive models in high-dimensional settings. We rigorously analyze the estimation error of the estimate resulting from the proposed algorithm. In Chapter 4, we study a semiparametric extension of finite mixtures and introduce a framework for statistical inference that is well-suited to mixture model settings. We propose an efficient one-step estimator for estimating a general finite-dimensional summary of a component distribution and corresponding confidence intervals.