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Mathematical Foundations of Infinite-Dimensional Statistical Models (Cambridge Series in Statistical and Probabilistic Mathematics, Series Number 40) by Evarist Giné, University of Connecticut, Richard Nickl, University of Cambridge is a nonfiction available to read on EtoBox.
What is Mathematical Foundations of Infinite-Dimensional Statistical Models (Cambridge Series in Statistical and Probabilistic Mathematics, Series Number 40) about?
Main subject categories: • Nonparametric statistics • High-dimensional statistics • Infinite-dimensional parameter spaces • Statistical inferenceIn 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, an
Who reads Mathematical Foundations of Infinite-Dimensional Statistical Models (Cambridge Series in Statistical and Probabilistic Mathematics, Series Number 40)?
It is typically read by self-directed learners exploring a subject in depth.
Common subject areas: history, science, philosophy, social sciences.
- Author
- Evarist Giné, University of Connecticut, Richard Nickl, University of Cambridge
- Publisher
- Cambridge University Press [CUP]
- Published
- 2016
- Language
- EN
- ISBN
- 9781316443880
- Category
- nonfiction
- Subjects
- Mathematics, Mathematical Statistics, Stem
Other editions & translations
- Mathematical Foundations of Infinite-Dimensional Statistical Models (Cambridge Series in Statistical and Probabilistic Mathematics, Series Number 40) (2015)
- Mathematical Foundations of Infinite-Dimensional Statistical Models (Cambridge Series in Statistical and Probabilistic Mathematics, Series Number 40) (2021)
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