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:
| Beteilige Person: | |
|---|---|
| Weitere beteiligte Personen: | |
| Format: | E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2021
|
| Ausgabe: | Revised edition. |
| Schriftenreihe: | Cambridge series in statistical and probabilistic mathematics
|
| Links: | https://doi.org/10.1017/9781009022811 |
| 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. |
| Umfang: | 1 Online-Ressource (xiv, 690 Seiten) |
| ISBN: | 9781009022811 |
Internformat
MARC
| LEADER | 00000nam a2200000 i 4500 | ||
|---|---|---|---|
| 001 | ZDB-20-CTM-CR9781009022811 | ||
| 003 | UkCbUP | ||
| 005 | 20210408230443.0 | ||
| 006 | m|||||o||d|||||||| | ||
| 007 | cr|||||||||||| | ||
| 008 | 201119s2021||||enk o ||1 0|eng|d | ||
| 020 | |a 9781009022811 | ||
| 100 | 1 | |a Giné, Evarist | |
| 245 | 1 | 0 | |a Mathematical foundations of infinite-dimensional statistical models |c Evarist Giné, Richard Nickl |
| 250 | |a Revised edition. | ||
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 2021 | |
| 300 | |a 1 Online-Ressource (xiv, 690 Seiten) | ||
| 336 | |b txt | ||
| 337 | |b c | ||
| 338 | |b cr | ||
| 490 | 1 | |a Cambridge series in statistical and probabilistic mathematics | |
| 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. | ||
| 700 | 1 | |a Nickl, Richard |d 1980- | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |z 9781108994132 |
| 966 | 4 | 0 | |l DE-91 |p ZDB-20-CTM |q TUM_PDA_CTM |u https://doi.org/10.1017/9781009022811 |3 Volltext |
| 912 | |a ZDB-20-CTM | ||
| 912 | |a ZDB-20-CTM | ||
| 049 | |a DE-91 | ||
Datensatz im Suchindex
| DE-BY-TUM_katkey | ZDB-20-CTM-CR9781009022811 |
|---|---|
| _version_ | 1825574046739202048 |
| adam_text | |
| any_adam_object | |
| author | Giné, Evarist |
| author2 | Nickl, Richard 1980- |
| author2_role | |
| author2_variant | r n rn |
| author_facet | Giné, Evarist Nickl, Richard 1980- |
| author_role | |
| author_sort | Giné, Evarist |
| author_variant | e g eg |
| building | Verbundindex |
| bvnumber | localTUM |
| collection | ZDB-20-CTM |
| edition | Revised edition. |
| format | eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02012nam a2200277 i 4500</leader><controlfield tag="001">ZDB-20-CTM-CR9781009022811</controlfield><controlfield tag="003">UkCbUP</controlfield><controlfield tag="005">20210408230443.0</controlfield><controlfield tag="006">m|||||o||d||||||||</controlfield><controlfield tag="007">cr||||||||||||</controlfield><controlfield tag="008">201119s2021||||enk o ||1 0|eng|d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781009022811</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Giné, Evarist</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Mathematical foundations of infinite-dimensional statistical models</subfield><subfield code="c">Evarist Giné, Richard Nickl</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">Revised edition.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge</subfield><subfield code="b">Cambridge University Press</subfield><subfield code="c">2021</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (xiv, 690 Seiten)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Cambridge series in statistical and probabilistic mathematics</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="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.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Nickl, Richard</subfield><subfield code="d">1980-</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe</subfield><subfield code="z">9781108994132</subfield></datafield><datafield tag="966" ind1="4" ind2="0"><subfield code="l">DE-91</subfield><subfield code="p">ZDB-20-CTM</subfield><subfield code="q">TUM_PDA_CTM</subfield><subfield code="u">https://doi.org/10.1017/9781009022811</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-20-CTM</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-20-CTM</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91</subfield></datafield></record></collection> |
| id | ZDB-20-CTM-CR9781009022811 |
| illustrated | Not Illustrated |
| indexdate | 2025-03-03T11:58:01Z |
| institution | BVB |
| isbn | 9781009022811 |
| language | English |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM |
| owner_facet | DE-91 DE-BY-TUM |
| physical | 1 Online-Ressource (xiv, 690 Seiten) |
| psigel | ZDB-20-CTM TUM_PDA_CTM ZDB-20-CTM |
| publishDate | 2021 |
| publishDateSearch | 2021 |
| publishDateSort | 2021 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Cambridge series in statistical and probabilistic mathematics |
| spelling | Giné, Evarist 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 c cr Cambridge series in statistical and probabilistic mathematics 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. Nickl, Richard 1980- Erscheint auch als Druck-Ausgabe 9781108994132 |
| spellingShingle | Giné, Evarist Mathematical foundations of infinite-dimensional statistical models |
| 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_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 |
| work_keys_str_mv | AT gineevarist mathematicalfoundationsofinfinitedimensionalstatisticalmodels AT nicklrichard mathematicalfoundationsofinfinitedimensionalstatisticalmodels |