Introduction to High-Dimensional Statistics

<p><strong>Praise for the first edition:</strong></p><p>[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.<br>—<b><em>Journal of the American Statistical Association</em></b></p><p>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:</p><ul> <p> </p> <li>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.</li> <p> </p> <li>Introduces three new chapters on iterative algorithms clustering and minimax lower bounds.</li> <p> </p> <li>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.</li> <p> </p> <li>Covers cutting-edge statistical methods including model selection sparsity and the Lasso iterative hard thresholding aggregation support vector machines and learning theory.</li> <p> </p> <li>Provides detailed exercises at the end of every chapter with collaborative solutions on a wiki site.</li> <p> </p> <li>Illustrates concepts with simple but clear practical examples.</li> </ul>