Articles liés à Theory of U-Statistics (Mathematics and Its Applications...
Synopsis
This monograph contains, for the first time, a systematic presentation of the theory of U-statistics. On the one hand, this theory is an extension of summation theory onto classes of dependent (in a special manner) random variables. On the other hand, the theory involves various statistical applications.
The construction of the theory is concentrated around the main asymptotic problems, namely, around the law of large numbers, the central limit theorem, the convergence of distributions of U-statistics with degenerate kernels, functional limit theorems, estimates for convergence rates, and asymptotic expansions. Probabilities of large deviations and laws of iterated logarithm are also considered. The connection between the asymptotics of U-statistics destributions and the convergence of distributions in infinite-dimensional spaces are discussed. Various generalizations of U-statistics for dependent multi-sample variables and for varying kernels are examined. When proving limit theorems and inequalities for the moments and characteristic functions the martingale structure of U-statistics and orthogonal decompositions are used. The book has ten chapters and concludes with an extensive reference list.
For researchers and students of probability theory and mathematical statistics.
Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.
Présentation de l'éditeur
This monograph contains, for the first time, a systematic presentation of the theory of U-statistics. On the one hand, this theory is an extension of summation theory onto classes of dependent (in a special manner) random variables. On the other hand, the theory involves various statistical applications.
The construction of the theory is concentrated around the main asymptotic problems, namely, around the law of large numbers, the central limit theorem, the convergence of distributions of U-statistics with degenerate kernels, functional limit theorems, estimates for convergence rates, and asymptotic expansions. Probabilities of large deviations and laws of iterated logarithm are also considered. The connection between the asymptotics of U-statistics destributions and the convergence of distributions in infinite-dimensional spaces are discussed. Various generalizations of U-statistics for dependent multi-sample variables and for varying kernels are examined. When proving limit theorems and inequalities for the moments and characteristic functions the martingale structure of U-statistics and orthogonal decompositions are used. The book has ten chapters and concludes with an extensive reference list.
For researchers and students of probability theory and mathematical statistics.
Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.
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Theory of U-Statistics (eng)
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Theory of U-Statistics (Mathematics and Its Applications, 273)
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Theory of U-Statistics
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Springer Netherlands, 2010
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Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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 intensivel. N° de réf. du vendeur 5818210
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Theory of U-Statistics
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Springer Netherlands, Springer Netherlands Dez 2010, 2010
ISBN 10 : 9048143462
ISBN 13 : 9789048143467
Neuf
Taschenbuch
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Taschenbuch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 568 pp. Englisch. N° de réf. du vendeur 9789048143467
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Theory of U-Statistics
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Taschenbuch. Etat : Neu. Theory of U-Statistics | Vladimir S. Korolyuk (u. a.) | Taschenbuch | x | Englisch | 2010 | Springer | EAN 9789048143467 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu. N° de réf. du vendeur 107174327
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Theory of U-Statistics
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Theory of U-Statistics
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Springer, Springer Dez 2010, 2010
ISBN 10 : 9048143462
ISBN 13 : 9789048143467
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Taschenbuch. Etat : Neu. This item is printed on demand - Print on Demand Titel. Neuware -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.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 568 pp. Englisch. N° de réf. du vendeur 9789048143467
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Taschenbuch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. N° de réf. du vendeur 9789048143467
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