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＜電子ブック＞
Theory of U-Statistics / by Vladimir S. Korolyuk, Y.V. Borovskich
(Mathematics and Its Applications ; 273)

版	1st ed. 1994.
出版者	(Dordrecht : Springer Netherlands : Imprint: Springer)
出版年	1994
本文言語	英語
大きさ	X, 554 p : online resource
著者標目	*Korolyuk, Vladimir S author Borovskich, Y.V author SpringerLink (Online service)
件　名	LCSH:Statistics  LCSH:Mathematical statistics -- Data processing  全ての件名で検索 FREE:Statistical Theory and Methods FREE:Statistics and Computing
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-94-017-3515-5

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