Theory of U-Statistics

Vladimir S. Korolyuk, Y.V. Borovskich (Autoren)

Buch | Softcover

554 Seiten

2010 | Softcover reprint of hardcover 1st ed. 1994
Springer (Verlag)
978-90-481-4346-7 (ISBN)

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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.

1. Basic Definitions and Notions.- 2. General Inequalities.- 3. The Law of Large Numbers.- 4. Weak Convergence.- 5. Functional Limit Theorems.- 6. Approximation in Limit Theorems.- 7. Asymptotic Expansions.- 8. Probabilities of Large Deviations.- 9. The Law of Iterated Logarithm.- 10. Dependent Variables.- Historical and bibliographical notes.- References.

Erscheint lt. Verlag	8.12.2010
Reihe/Serie	Mathematics and Its Applications ; 273
Zusatzinfo	X, 554 p.
Verlagsort	Dordrecht
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Computerprogramme / Computeralgebra
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
ISBN-10	90-481-4346-2 / 9048143462
ISBN-13	978-90-481-4346-7 / 9789048143467
Zustand	Neuware