Penalized Estimation of High Dimensional Models

This book is based on a course on penalized high-dimensional estimation that the author taught for second year graduate students in economics at Northwestern University. The book concentrates on ideas, methods, and results that are useful for empirical research in economics and related fields but avoids complicated mathematics and technical discussions. It explains why the results it presents are true, provides informal derivations of them, and presents some proofs. The book treats LASSO estimation of linear models and the properties of estimates obtained with the LASSO and several other penalization methods. It also treats nonlinear and conditional moment models, endogeneity and instrumental variables estimation, quantile models, and non- and semiparametric models. The treatment of inference includes bootstrap asymptotic refinements for linear and nonlinear models. In all cases, it aims at providing understanding without the difficult mathematics that are often part of discussions of these topics. The book avoids methods and results that involve complex mathematics that are not central to the main ideas underlying penalized estimation and that non-statisticians and non-econometricians often find inaccessible. It provides references to journal articles and books that treat mathematically difficult topics.Key Features:• Treats ideas, methods, and results that are useful for empirical research in economics and related fields but avoids complicated mathematics that non-statisticians and non-econometricians often find inaccessible.• Explains why the results it presents are true, provides informal derivations of them, and presents some proofs. • Treats penalized estimation of linear and nonlinear models, conditional moment models, endogeneity and instrumental variables estimation, quantile models, non- and semiparametric models, and bootstrap methods for inference. • Presents computational methods.• Includes exercises and computational problems.