Some approximation problems in statistics and probability

Авторы: Prokhorov Y.V., Ulyanov V.V.
Сборник: Springer Proceedings in Mathematics and Statistics
Том: 42
Год издания: 2013
Издательство: SPRINGER HEIDELBERG
Местоположение издательства: TIERGARTENSTRASSE 17, HEIDELBERG, GERMANY,D-69121
Первая страница: 235
Последняя страница: 249
DOI: 10.1007/978-3-642-36068-8_11
Аннотация: All three gems in probability theory -- the law of large numbers, the central limit theorem and the law of the iterated logarithm -- concern the asymptotic behavior of the sums of random variables. It would be natural to extend the results to the functionals of the sums, in particular to quadratic forms. Moreover, in mathematical statistics there are numerous asymptotic problems which can be formulated in terms of quadratic or almost quadratic forms. In this article we review the corresponding results with rates of convergence. Some of these results are optimal and could not be further improved without additional conditions. The review does not pretend to completely illuminate the present state of the area under consideration. It reflects mainly the authors interests.
Добавил в систему: Ульянов Владимир Васильевич

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