Based on courses taught at the University of Cambridge, this text presents core contemporary statistical methods and theory in an accessible, self-contained and rigorous fashion, with a focus on finite-sample guarantees as opposed to asymptotic arguments. Many of the topics and results have not appeared in book form previously, and some constitute new research. The prerequisites are relatively light (primarily a good grasp of linear algebra and real analysis) and complete solutions to all 250+ exercises are available online. It is the perfect entry point to the subject for master's and graduate-level students in statistics, data science and machine learning, as well as related disciplines such as artificial intelligence, signal processing, information theory, electrical engineering and econometrics. Researchers in these fields will also find it an invaluable resource. This title is also available as Open Access on Cambridge Core.

‘This is a very comprehensive and rigorous graduate text that synthesises key ideas across modern statistics. Its clear exposition and broad, carefully chosen topics make it invaluable for students and researchers seeking a deep and unified understanding of modern statistical theory and methods.’

Jianqing Fan - Princeton University

‘This text provides an excellent account of modern topics in statistical inference. With an emphasis on topics of great current importance, such as high-dimensional models, causality and shape-constrained methods, the book is perfect for students and for researchers.’

Larry Wasserman - Carnegie Mellon University

‘A masterful synthesis that reshapes how we think about high-dimensional inference, bringing theoretical coherence to a large set of statistical problems that are routinely encountered in practice. Samworth and Shah write with intellectual élan, mathematical rigour and conceptual clarity, inspiring researchers to push the boundaries of what's possible next in modern statistical inference. Essential reading for anyone seeking to understand the mathematical foundations of modern statistics in the age of large, complex data streams.’

Bhramar Mukherjee - Yale School of Public Health

‘This excellent book offers a clear and unifying description of nonparametric statistics, high-dimensional statistics and causality. The mathematical elegance of the exposition is truly impressive. Self-contained and rich in exercises, it is ideal for self-study, as a foundation for courses and as a reliable reference for researchers. Highly recommended.’

Johannes Schmidt-Hieber - University of Twente

‘A beautiful tour de force of modern statistical theory. From high-dimensional regression and kernel methods to shape-constrained inference and causality, the authors offer a clear and coherent account in the finest Cambridge tradition – mathematically elegant, conceptually illuminating and invaluable to graduate students and researchers.’

Yuting Wei - University of Pennsylvania

‘This book offers a well-curated tour of contemporary statistical topics from a non-asymptotic theory perspective. The treatment is driven by methodology rather than stylised abstraction, with clarity and purpose throughout. Breadth and depth are finely calibrated, resulting in an eminently teachable and thoughtfully self-contained text.’

Victor Panaretos - EPFL

‘Rarely have I encountered a book that makes modern statistics feel at once so deep and so teachable. Rigorous, wide-ranging and beautifully judged, it offers insights that will remain with readers long after the final page.’

Olga Klopp - ESSEC Business School

‘An ideal companion for graduate courses at an intermediate to advanced level with a very cleverly organised syllabus, starting from basic statistical theory for linear models, and ending with more specialised topics on shape-constrained estimation. As a whole, the text covers many timely and important must-haves of modern mathematical statistics. The careful explanation of ideas and the thoroughly worked out interplay between examples and theory make reading an enjoyment. This book bridges a variety of textbooks that are devoted to more specialised topics in mathematical statistics with those that merely focus on methodology and applications.’

Axel Munk - University of Göttingen