Mathematical Foundations of Infinite-Dimensional Statistical Models

ISBN-13: 9781108994132 / Angielski / Miękka / 2021 / 704 str.

Richard (University of Cambridge) Nickl

Opis

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.

Spis treści

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.