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Theory of U-Statistics (Mathematics and Its Applications)

Vladimir S. Korolyuk

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ISBN 10: 9048143462 / ISBN 13: 9789048143467
Published by Springer, 2010
New Condition: New Soft cover
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Title: Theory of U-Statistics (Mathematics and Its ...

Publisher: Springer

Publication Date: 2010

Binding: Paperback

Book Condition:New

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Synopsis:

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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