Theory of U-Statistics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1994
|
| Schriftenreihe: | Mathematics and Its Applications
273 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The theory of U-statistics goes back to the fundamental work of Hoeffding [1], in which he proved the central limit theorem. During last forty years the interest to this class of random variables has been permanently increasing, and thus, the new intensively developing branch of probability theory has been formed. The U-statistics are one of the universal objects of the modem probability theory of summation. On the one hand, they are more complicated "algebraically" than sums of independent random variables and vectors, and on the other hand, they contain essential elements of dependence which display themselves in the martingale properties. In addition, the U -statistics as an object of mathematical statistics occupy one of the central places in statistical problems. The development of the theory of U-statistics is stipulated by the influence of the classical theory of summation of independent random variables: The law of large num bers, central limit theorem, invariance principle, and the law of the iterated logarithm we re proved, the estimates of convergence rate were obtained, etc |
| Beschreibung: | 1 Online-Ressource (X, 554 p) |
| ISBN: | 9789401735155 9789048143467 |
| DOI: | 10.1007/978-94-017-3515-5 |
Internformat
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| 490 | 0 | |a Mathematics and Its Applications |v 273 | |
| 500 | |a The theory of U-statistics goes back to the fundamental work of Hoeffding [1], in which he proved the central limit theorem. During last forty years the interest to this class of random variables has been permanently increasing, and thus, the new intensively developing branch of probability theory has been formed. The U-statistics are one of the universal objects of the modem probability theory of summation. On the one hand, they are more complicated "algebraically" than sums of independent random variables and vectors, and on the other hand, they contain essential elements of dependence which display themselves in the martingale properties. In addition, the U -statistics as an object of mathematical statistics occupy one of the central places in statistical problems. The development of the theory of U-statistics is stipulated by the influence of the classical theory of summation of independent random variables: The law of large num bers, central limit theorem, invariance principle, and the law of the iterated logarithm we re proved, the estimates of convergence rate were obtained, etc | ||
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Datensatz im Suchindex
| _version_ | 1804153101152681984 |
|---|---|
| any_adam_object | |
| author | Koroljuk, V. S. |
| author_facet | Koroljuk, V. S. |
| author_role | aut |
| author_sort | Koroljuk, V. S. |
| author_variant | v s k vs vsk |
| building | Verbundindex |
| bvnumber | BV042424325 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)1165486413 (DE-599)BVBBV042424325 |
| dewey-full | 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 |
| dewey-search | 519.5 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-017-3515-5 |
| format | Electronic eBook |
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| id | DE-604.BV042424325 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:15Z |
| institution | BVB |
| isbn | 9789401735155 9789048143467 |
| language | English |
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| physical | 1 Online-Ressource (X, 554 p) |
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| publishDate | 1994 |
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| publisher | Springer Netherlands |
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| series2 | Mathematics and Its Applications |
| spelling | Koroljuk, V. S. Verfasser aut Theory of U-Statistics by V. S. Koroljuk, Yu. V. Borovskich Dordrecht Springer Netherlands 1994 1 Online-Ressource (X, 554 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 273 The theory of U-statistics goes back to the fundamental work of Hoeffding [1], in which he proved the central limit theorem. During last forty years the interest to this class of random variables has been permanently increasing, and thus, the new intensively developing branch of probability theory has been formed. The U-statistics are one of the universal objects of the modem probability theory of summation. On the one hand, they are more complicated "algebraically" than sums of independent random variables and vectors, and on the other hand, they contain essential elements of dependence which display themselves in the martingale properties. In addition, the U -statistics as an object of mathematical statistics occupy one of the central places in statistical problems. The development of the theory of U-statistics is stipulated by the influence of the classical theory of summation of independent random variables: The law of large num bers, central limit theorem, invariance principle, and the law of the iterated logarithm we re proved, the estimates of convergence rate were obtained, etc Statistics Statistics, general Statistik Statistik (DE-588)4056995-0 gnd rswk-swf U-Statistik (DE-588)4754777-7 gnd rswk-swf U-Stichprobenfunktion (DE-588)4279548-5 gnd rswk-swf Grenzwertsatz (DE-588)4158163-5 gnd rswk-swf U-Stichprobenfunktion (DE-588)4279548-5 s 1\p DE-604 Grenzwertsatz (DE-588)4158163-5 s 2\p DE-604 U-Statistik (DE-588)4754777-7 s 3\p DE-604 Statistik (DE-588)4056995-0 s 4\p DE-604 Borovskich, Yu. V. Sonstige oth https://doi.org/10.1007/978-94-017-3515-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Koroljuk, V. S. Theory of U-Statistics Statistics Statistics, general Statistik Statistik (DE-588)4056995-0 gnd U-Statistik (DE-588)4754777-7 gnd U-Stichprobenfunktion (DE-588)4279548-5 gnd Grenzwertsatz (DE-588)4158163-5 gnd |
| subject_GND | (DE-588)4056995-0 (DE-588)4754777-7 (DE-588)4279548-5 (DE-588)4158163-5 |
| title | Theory of U-Statistics |
| title_auth | Theory of U-Statistics |
| title_exact_search | Theory of U-Statistics |
| title_full | Theory of U-Statistics by V. S. Koroljuk, Yu. V. Borovskich |
| title_fullStr | Theory of U-Statistics by V. S. Koroljuk, Yu. V. Borovskich |
| title_full_unstemmed | Theory of U-Statistics by V. S. Koroljuk, Yu. V. Borovskich |
| title_short | Theory of U-Statistics |
| title_sort | theory of u statistics |
| topic | Statistics Statistics, general Statistik Statistik (DE-588)4056995-0 gnd U-Statistik (DE-588)4754777-7 gnd U-Stichprobenfunktion (DE-588)4279548-5 gnd Grenzwertsatz (DE-588)4158163-5 gnd |
| topic_facet | Statistics Statistics, general Statistik U-Statistik U-Stichprobenfunktion Grenzwertsatz |
| url | https://doi.org/10.1007/978-94-017-3515-5 |
| work_keys_str_mv | AT koroljukvs theoryofustatistics AT borovskichyuv theoryofustatistics |