Mathematical Foundations of Infinite-Dimensional Statistical Models

Now in paperback: the new classic on the theory of statistical inference in statistical models with an infinite-dimensional parameter space.

List of contents

Preface; 1. Nonparametric statistical models; 2. Gaussian processes; 3. Empirical processes; 4. Function spaces and approximation theory; 5. Linear nonparametric estimators; 6. The minimax paradigm; 7. Likelihood-based procedures; 8. Adaptive inference; References; Author Index; Index.

About the author

Evarist Giné (1944–2015) was Head of the Department of Mathematics at the University of Connecticut. Giné was a distinguished mathematician who worked on mathematical statistics and probability in infinite dimensions. He was the author of two books and more than 100 articles.Richard Nickl is Professor of Mathematical Statistics in the Statistical Laboratory within the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge.

Summary

High-dimensional and nonparametric statistical models are ubiquitous in modern data science. This book develops a mathematically coherent and objective approach to statistical inference in such models, with a focus on function estimation problems arising from random samples or from Gaussian regression/signal in white noise problems.

Product details

• Authors: Evarist Gine, Evarist Nickl Gine, Evarist Giné, Richard Nickl, Richard (University of Cambridge) Nickl, Nickl Richard
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Paperback / Softback
• Released: 30.04.2021
• EAN: 9781108994132
• ISBN: 978-1-108-99413-2
• No. of pages: 704
• Series: Cambridge Series in Statistical and Probabilistic Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; Social sciences, law, business > Business > General, dictionaries; machine learning, MATHEMATICS / Probability & Statistics / General, Signal Processing, Probability & statistics, Calculus & mathematical analysis, Econometrics, Probability and statistics, Calculus and mathematical analysis, Econometrics and economic statistics, Digital signal processing (DSP)