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Theory of U-Statistics (Mathematics and Its Applications)

Amazon.com Price: $145.51 (as of 01/05/2019 14:44 PST- Details)

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The theory of U-statistics goes back to the fundamental work of Hoeffding [1], through which he proved the central limit theorem. All through 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 some of the universal objects of the modem probability theory of summation. At the one hand, they’re more complicated “algebraically” than sums of independent random variables and vectors, and then again, they contain crucial elements of dependence which display themselves within the martingale properties. As well as, the U -statistics as an object of mathematical statistics occupy some 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, and so on.

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Theory of U-Statistics (Mathematics and Its Applications)

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