Praise for the first edition:
"[This book] succeeds singularly at providing a structured
introduction to this active field of research. ... it is arguably the
most accessible overview yet published of the mathematical ideas and
principles that one needs to master to enter the field of
high-dimensional statistics. ... recommended to anyone interested in the
main results of current research in high-dimensional statistics as well
as anyone interested in acquiring the core mathematical skills to enter
this area of research."
--Journal of the American Statistical Association
Introduction to High-Dimensional Statistics, Second Edition preserves
the philosophy of the first edition: to be a concise guide for students
and researchers discovering the area and interested in the mathematics
involved. The main concepts and ideas are presented in simple settings,
avoiding thereby unessential technicalities. High-dimensional statistics
is a fast-evolving field, and much progress has been made on a large
variety of topics, providing new insights and methods. Offering a
succinct presentation of the mathematical foundations of
high-dimensional statistics, this new edition:
- Offers revised chapters from the previous edition, with the inclusion
of many additional materials on some important topics, including
compress sensing, estimation with convex constraints, the slope
estimator, simultaneously low-rank and row-sparse linear regression,
or aggregation of a continuous set of estimators.
- Introduces three new chapters on iterative algorithms, clustering, and
minimax lower bounds.
- Provides enhanced appendices, minimax lower-bounds mainly with the
addition of the Davis-Kahan perturbation bound and of two simple
versions of the Hanson-Wright concentration inequality.
- Covers cutting-edge statistical methods including model selection,
sparsity and the Lasso, iterative hard thresholding, aggregation,
support vector machines, and learning theory.
- Provides detailed exercises at the end of every chapter with
collaborative solutions on a wiki site.
- Illustrates concepts with simple but clear practical examples.
