Semiparametric Theory and Missing Data

Missing data arise in almost all scientific disciplines. In many cases, the treatment of missing data in an analysis is carried out in a casual and ad-hoc manner, leading, in many cases, to invalid inference and erroneous conclusions. In the past 20 years or so, there has been a serious attempt to understand the underlying issues and difficulties that come about from missing data and their impact on subsequent analysis. There has been a great deal written on the theory developed for analyzing missing data for finite-dimensional parametric models. This includes an extensive literature on likelihood-based methods and multiple imputation. More recently, there has been increasing interest in semiparametric models which, roughly speaking, are models that include both a parametric and nonparametric component. Such models are popular because estimators in such models are more robust than in traditional parametric models. The theory of missing data applied to semiparametric models is scattered throughout the literature with no thorough comprehensive treatment of the subject.

This book combines much of what is known in regard to 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 at a level that 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.

List of contents

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.

Summary

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.

Additional text

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 usefulfor graduate and post-graduate students in statistics and biostatistics, as well as researchers in statistics and survival analysis." (Oleksandr Kukush, Zentralblatt MATH, Vol. 1105 (7), 2007)

Report

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 usefulfor graduate and post-graduate students in statistics and biostatistics, as well as researchers in statistics and survival analysis." (Oleksandr Kukush, Zentralblatt MATH, Vol. 1105 (7), 2007)

Product details

• Authors: Anastasios Tsiatis, Anastasios A. Tsiatis
• Publisher: Springer, Berlin
• Languages: English
• Product format: Hardback
• Released: 19.07.2006
• EAN: 9780387324487
• ISBN: 978-0-387-32448-7
• No. of pages: 388
• Dimensions: 156 mm x 28 mm x 241 mm
• Weight: 768 g
• Illustrations: XVI, 388 p.
• Series: Springer Series in Statistics; Springer Texts in Statistics; Springer Texts in Statistics; Springer Series in Statistics
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics