Introduction

Abstract

In most empirical studies, the full (equivalently, complete) data X on certain subjects are censored (equivalently, missing or coarsened). That is, the data X that one would wish to collect are incompletely observed for a (possibly improper) subset of the study subjects; instead, only a random function (equivalently, a random coarsening) Y of X is observed. Furthermore, over the past decades, data from epidemiological, biostatistical, and econometric studies have become increasingly high-dimensional as longitudinal designs that collect data on many time-varying covariate processes at frequent intervals have become commonplace. Scientific interest, however, often focuses on a low-dimensional functional μ of the distribution F _X of the full data — say, as an example, the medians of the treatment-arm specific distributions of time to tumor recurrence in a cancer clinical trial in which recurrence times are right censored by lost -to-follow-up. In such a trial, X is often high dimesional because the study protocol specifies comprehensive laboratory and clinical measurements be taken monthly. In such settings, the use of non-or semiparametric models for F _X that do not model the components of F _X that are of little scientific interest have become commonplace, so as to insure that misspecification of the functional form of a parametric model for the entire distribution F _X does not induce biased estimates of μ. The methodology described in this book was developed to meet the analytic challenges posed by high dimensional censored data in which a low-dimensional functional μ of the distribution F _X is the parameter of scientific interest.