Semiparametric Theory and Missing Data

to Semiparametric Models.- Hilbert Space for Random Vectors.- The Geometry of Influence Functions.- Semiparametric Models.- Other Examples of Semiparametric Models.- Models and Methods for Missing Data.- Missing and Coarsening at Random for Semiparametric Models.- The Nuisance Tangent Space and Its Orthogonal Complement.- Augmented Inverse Probability Weighted Complete-Case Estimators.- Improving Efficiency and Double Robustness with Coarsened Data.- Locally Efficient Estimators for Coarsened-Data Semiparametric Models.- Approximate Methods for Gaining Efficiency.- Double-Robust Estimator of the Average Causal Treatment Effect.- Multiple Imputation: A Frequentist Perspective.

Missing data arise in almost all scientific disciplines. In many cases, missing data in an analysis is treated in a casual and ad-hoc manner, leading to invalid inferences and erroneous conclusions. The past 20 years have seen a serious attempt to understand the underlying issues and difficulties arising from missing data and their impact on subsequent analysis. This book summarizes current knowledge regarding the theory of estimation for semiparametric models with missing data, in an organized and comprehensive manner. It starts with the study of semiparametric methods when there are no missing data. The description of the theory of estimation for semiparametric models is both rigorous and intuitive, relying on geometric ideas to reinforce the intuition and understanding of the theory. These methods are then applied to problems with missing, censored, and coarsened data with the goal of deriving estimators that are as robust and efficient as possible.

From the reviews:

"The author, who does not need an introduction...had presented with clarity how he views three different subjects within a unified approach for statistical inference....It is a long awaited book for a large audience of graduate students and researchers who have often found this subject matter daunting.... It is an easy decision for me to recommend this book to anyone who is interested in learning and using theories of frequentist estimation for semiparametric models and coarsened data. Even beyond his/her graduate student days, any statistical researcher interested in mastering frequentist semiparamatric estimation can pick up all the essential information from this book." (Debajyoti Sinha, American Statistical Association, JASA, March 2009, Vol. 104, No. 485)

"Since much of the work in this area is very technical, it is most welcome to have a self-contained clearly written account by a highly-regarded author. The application to missing data is also clearly of great interest." R.J.A. Little for Short Book Reviews of the ISI, December 2006

"This book is focused precisely on the problem of estimation for a semiparametric model when the data are missing. This comprehensive monograph offers an in-depth look at the associated theory ... . It was a great pleasure to read this masterful account of semiparametric theory for missing data problems ... . It provides a valuable resource because it contains an up-to-date literature review and an exceptional account of state of the art research on the necessary theory. ... I recommend it to any professional statistician." (Konstantinos Fokianos, Technometrics, Vol. 49 (2), 2007)

"The book under review deals with estimation for SMs with missing, coarsened, and censored data. ... The book is very clearly and informally written. The exposition is instructive and rigorous enough. There are many important examples, oriented to biomedical applications. The monograph will be