Mathematical foundations of infinite-dimensional statistical models:
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 cohe...
Gespeichert in:
| Hauptverfasser: | , |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2021
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| Ausgabe: | Revised edition |
| Schriftenreihe: | Cambridge series in statistical and probabilistic mathematicss
|
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 TUM01 URL des Erstveröffentlichers |
| Zusammenfassung: | 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, approximation and wavelet theory, and the basic theory of function spaces. The theory of statistical inference in such models - hypothesis testing, estimation and confidence sets - is 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. Winner of the 2017 PROSE Award for Mathematics |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 08 Mar 2021) |
| Beschreibung: | 1 Online-Ressource (xiv, 690 Seiten) |
| ISBN: | 9781009022811 |
| DOI: | 10.1017/9781009022811 |
Internformat
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| 520 | |a 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, approximation and wavelet theory, and the basic theory of function spaces. The theory of statistical inference in such models - hypothesis testing, estimation and confidence sets - is 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. Winner of the 2017 PROSE Award for Mathematics | ||
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Datensatz im Suchindex
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| dewey-full | 519.5/4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/4 |
| dewey-search | 519.5/4 |
| dewey-sort | 3519.5 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| doi_str_mv | 10.1017/9781009022811 |
| edition | Revised edition |
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| id | DE-604.BV047291968 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T17:20:26Z |
| indexdate | 2024-07-10T09:07:59Z |
| institution | BVB |
| isbn | 9781009022811 |
| language | English |
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| physical | 1 Online-Ressource (xiv, 690 Seiten) |
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| spelling | Giné, Evarist 1944-2015 (DE-588)128482494 aut Mathematical foundations of infinite-dimensional statistical models Evarist Giné, Richard Nickl Revised edition Cambridge Cambridge University Press 2021 1 Online-Ressource (xiv, 690 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge series in statistical and probabilistic mathematicss Title from publisher's bibliographic system (viewed on 08 Mar 2021) 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, approximation and wavelet theory, and the basic theory of function spaces. The theory of statistical inference in such models - hypothesis testing, estimation and confidence sets - is 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. Winner of the 2017 PROSE Award for Mathematics Nonparametric statistics Function spaces Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Nichtparametrisches Modell (DE-588)4434654-2 gnd rswk-swf Nichtparametrisches Modell (DE-588)4434654-2 s Stochastischer Prozess (DE-588)4057630-9 s DE-604 Nickl, Richard 1980- (DE-588)1083823582 aut Erscheint auch als Druck-Ausgabe 978-1-108-99413-2 https://doi.org/10.1017/9781009022811 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Giné, Evarist 1944-2015 Nickl, Richard 1980- Mathematical foundations of infinite-dimensional statistical models Nonparametric statistics Function spaces Stochastischer Prozess (DE-588)4057630-9 gnd Nichtparametrisches Modell (DE-588)4434654-2 gnd |
| subject_GND | (DE-588)4057630-9 (DE-588)4434654-2 |
| title | Mathematical foundations of infinite-dimensional statistical models |
| title_auth | Mathematical foundations of infinite-dimensional statistical models |
| title_exact_search | Mathematical foundations of infinite-dimensional statistical models |
| title_exact_search_txtP | Mathematical foundations of infinite-dimensional statistical models |
| title_full | Mathematical foundations of infinite-dimensional statistical models Evarist Giné, Richard Nickl |
| title_fullStr | Mathematical foundations of infinite-dimensional statistical models Evarist Giné, Richard Nickl |
| title_full_unstemmed | Mathematical foundations of infinite-dimensional statistical models Evarist Giné, Richard Nickl |
| title_short | Mathematical foundations of infinite-dimensional statistical models |
| title_sort | mathematical foundations of infinite dimensional statistical models |
| topic | Nonparametric statistics Function spaces Stochastischer Prozess (DE-588)4057630-9 gnd Nichtparametrisches Modell (DE-588)4434654-2 gnd |
| topic_facet | Nonparametric statistics Function spaces Stochastischer Prozess Nichtparametrisches Modell |
| url | https://doi.org/10.1017/9781009022811 |
| work_keys_str_mv | AT gineevarist mathematicalfoundationsofinfinitedimensionalstatisticalmodels AT nicklrichard mathematicalfoundationsofinfinitedimensionalstatisticalmodels |