Reproducing Kernel Hilbert Spaces in Probability and Statistics:
The reproducing kernel Hilbert space construction is a bijection or transform theory which associates a positive definite kernel (gaussian processes) with a Hilbert space offunctions. Like all transform theories (think Fourier), problems in one space may become transparent in the other, and optimal...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer US
2004
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| Ausgabe: | 1st ed. 2004 |
| Schlagworte: | |
| Online-Zugang: | BTU01 Volltext |
| Zusammenfassung: | The reproducing kernel Hilbert space construction is a bijection or transform theory which associates a positive definite kernel (gaussian processes) with a Hilbert space offunctions. Like all transform theories (think Fourier), problems in one space may become transparent in the other, and optimal solutions in one space are often usefully optimal in the other. The theory was born in complex function theory, abstracted and then accidently injected into Statistics; Manny Parzen as a graduate student at Berkeley was given a strip of paper containing his qualifying exam problem- It read "reproducing kernel Hilbert space"- In the 1950's this was a truly obscure topic. Parzen tracked it down and internalized the subject. Soon after, he applied it to problems with the following fla vor: consider estimating the mean functions of a gaussian process. The mean functions which cannot be distinguished with probability one are precisely the functions in the Hilbert space associated to the covariance kernel of the processes. Parzen's own lively account of his work on re producing kernels is charmingly told in his interview with H. Joseph Newton in Statistical Science, 17, 2002, p. 364-366. Parzen moved to Stanford and his infectious enthusiasm caught Jerry Sacks, Don Ylvisaker and Grace Wahba among others. Sacks and Ylvis aker applied the ideas to design problems such as the following. Sup pose (XdO. |
| Beschreibung: | 1 Online-Ressource (XXII, 355 p) |
| ISBN: | 9781441990969 |
| DOI: | 10.1007/978-1-4419-9096-9 |
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| author | Berlinet, Alain Thomas-Agnan, Christine |
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| discipline | Mathematik Wirtschaftswissenschaften |
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| edition | 1st ed. 2004 |
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| index_date | 2024-07-03T15:15:38Z |
| indexdate | 2024-07-10T08:56:11Z |
| institution | BVB |
| isbn | 9781441990969 |
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| spelling | Berlinet, Alain Verfasser aut Reproducing Kernel Hilbert Spaces in Probability and Statistics by Alain Berlinet, Christine Thomas-Agnan 1st ed. 2004 New York, NY Springer US 2004 1 Online-Ressource (XXII, 355 p) txt rdacontent c rdamedia cr rdacarrier The reproducing kernel Hilbert space construction is a bijection or transform theory which associates a positive definite kernel (gaussian processes) with a Hilbert space offunctions. Like all transform theories (think Fourier), problems in one space may become transparent in the other, and optimal solutions in one space are often usefully optimal in the other. The theory was born in complex function theory, abstracted and then accidently injected into Statistics; Manny Parzen as a graduate student at Berkeley was given a strip of paper containing his qualifying exam problem- It read "reproducing kernel Hilbert space"- In the 1950's this was a truly obscure topic. Parzen tracked it down and internalized the subject. Soon after, he applied it to problems with the following fla vor: consider estimating the mean functions of a gaussian process. The mean functions which cannot be distinguished with probability one are precisely the functions in the Hilbert space associated to the covariance kernel of the processes. Parzen's own lively account of his work on re producing kernels is charmingly told in his interview with H. Joseph Newton in Statistical Science, 17, 2002, p. 364-366. Parzen moved to Stanford and his infectious enthusiasm caught Jerry Sacks, Don Ylvisaker and Grace Wahba among others. Sacks and Ylvis aker applied the ideas to design problems such as the following. Sup pose (XdO. Economics, general Statistics for Business, Management, Economics, Finance, Insurance Economic Theory/Quantitative Economics/Mathematical Methods Economics Management science Statistics Economic theory Statistik (DE-588)4056995-0 gnd rswk-swf Kernfunktion (DE-588)4163607-7 gnd rswk-swf Hilbert-Raum (DE-588)4159850-7 gnd rswk-swf Hilbert-Raum (DE-588)4159850-7 s Kernfunktion (DE-588)4163607-7 s Statistik (DE-588)4056995-0 s DE-604 Thomas-Agnan, Christine aut Erscheint auch als Druck-Ausgabe 9781461347927 Erscheint auch als Druck-Ausgabe 9781402076794 Erscheint auch als Druck-Ausgabe 9781441990976 https://doi.org/10.1007/978-1-4419-9096-9 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Berlinet, Alain Thomas-Agnan, Christine Reproducing Kernel Hilbert Spaces in Probability and Statistics Economics, general Statistics for Business, Management, Economics, Finance, Insurance Economic Theory/Quantitative Economics/Mathematical Methods Economics Management science Statistics Economic theory Statistik (DE-588)4056995-0 gnd Kernfunktion (DE-588)4163607-7 gnd Hilbert-Raum (DE-588)4159850-7 gnd |
| subject_GND | (DE-588)4056995-0 (DE-588)4163607-7 (DE-588)4159850-7 |
| title | Reproducing Kernel Hilbert Spaces in Probability and Statistics |
| title_auth | Reproducing Kernel Hilbert Spaces in Probability and Statistics |
| title_exact_search | Reproducing Kernel Hilbert Spaces in Probability and Statistics |
| title_exact_search_txtP | Reproducing Kernel Hilbert Spaces in Probability and Statistics |
| title_full | Reproducing Kernel Hilbert Spaces in Probability and Statistics by Alain Berlinet, Christine Thomas-Agnan |
| title_fullStr | Reproducing Kernel Hilbert Spaces in Probability and Statistics by Alain Berlinet, Christine Thomas-Agnan |
| title_full_unstemmed | Reproducing Kernel Hilbert Spaces in Probability and Statistics by Alain Berlinet, Christine Thomas-Agnan |
| title_short | Reproducing Kernel Hilbert Spaces in Probability and Statistics |
| title_sort | reproducing kernel hilbert spaces in probability and statistics |
| topic | Economics, general Statistics for Business, Management, Economics, Finance, Insurance Economic Theory/Quantitative Economics/Mathematical Methods Economics Management science Statistics Economic theory Statistik (DE-588)4056995-0 gnd Kernfunktion (DE-588)4163607-7 gnd Hilbert-Raum (DE-588)4159850-7 gnd |
| topic_facet | Economics, general Statistics for Business, Management, Economics, Finance, Insurance Economic Theory/Quantitative Economics/Mathematical Methods Economics Management science Statistics Economic theory Statistik Kernfunktion Hilbert-Raum |
| url | https://doi.org/10.1007/978-1-4419-9096-9 |
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