Tsiatis A. Semiparametric Theory and Missing Data

Springer, 2006. — 384 p. — ISBN: 0387324488, 978-0387324487.
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.Introduction 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.