Modern Statistical Methods and Theory

An Introduction to Nonparametric and High-Dimensional Statistics
Erscheinungsjahr 2026
ISBN: 978-1-009-16043-8
Verlag: Cambridge University Press

Buch, Englisch, 450 Seiten

Reihe: Cambridge Series in Statistical and Probabilistic Mathematics

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.

Autoren/Hrsg.

Samworth, Richard J.

Shah, Rajen D.

Inhaltsverzeichnis

Acknowledgements; 1. Introduction; 2. Linear models and ordinary least squares; 3. High-dimensional linear regression; 4. Kernel density estimation; 5. Nonparametric regression; 6. Reproducing kernel Hilbert spaces and kernel machines; 7. Conditional independence, graphical models and causality; 8. Minimax lower bounds; 9. Shape-constrained estimation; Appendix. Basic tools; References; Index.

Über Autor(innen)

Shah, Rajen D.
Rajen D. Shah is Professor of Statistics at the University of Cambridge. He was awarded the Royal Statistical Society Research Prize (2017) and its Guy Medal in Bronze (2022), and he was elected a Fellow of the Institute of Mathematical Statistics (2025). He serves as Associate Editor for the 'Journal of the Royal Statistical Society: Series B', 'The Annals of Statistics' and 'Biometrika'.

Samworth, Richard J.
Richard J. Samworth is Professor of Statistical Science at the University of Cambridge. Among other honours, he received the COPSS Presidents' Award (2018), was elected a Fellow of the Royal Society (2021) and was awarded the David Cox Medal for Statistics (2025). He served as co-editor of 'The Annals of Statistics' (2019–2021) and is President-Elect of the Institute of Mathematical Statistics.