Mathematical Foundations of Infinite-Dimensional Statistical Models
Mathematical Foundations of Infinite-Dimensional Statistical Models
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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.
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Mathematical Foundations of Infinite-Dimensional Statistical Models by Evarist Gin
In nonparametric and high-dimensional statistical models, the classical Gauss-Fisher-Le Cam theory of the optimality of maximum likelihood estimators and Bayesian posterior inference does not apply, and new foundations and ideas have been developed in the past several decades. This book gives a coherent account of the statistical theory in infinite-dimensional parameter spaces. The mathematical foundations include self-contained 'mini-courses' on the theory of Gaussian and empirical processes, on approximation and wavelet theory, and on the basic theory of function spaces. The theory of statistical inference in such models - hypothesis testing, estimation and confidence sets - is then presented within the minimax paradigm of decision theory. This includes the basic theory of convolution kernel and projection estimation, but also Bayesian nonparametrics and nonparametric maximum likelihood estimation. In a final chapter the theory of adaptive inference in nonparametric models is developed, including Lepski's method, wavelet thresholding, and adaptive inference for self-similar functions.
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.
| SKU | Unavailable |
| ISBN 13 | 9781108994132 |
| ISBN 10 | 110899413X |
| Title | Mathematical Foundations of Infinite-Dimensional Statistical Models |
| Author | Evarist Gin |
| Series | Cambridge Series In Statistical And Probabilistic Mathematics |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | Cambridge University Press |
| Year published | 2021-03-25 |
| Number of pages | 704 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |