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Second-order Chebyshev–Edgeworth and Cornish–Fisher expansions for distributions of statistics constructed from samples with random sizesстатья
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Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 10 июня 2020 г.
- Авторы: Christoph G., Monakhov M.M., Ulyanov V.V.
- Журнал: Journal of Mathematical Sciences
- Том: 244
- Номер: 5
- Год издания: 2020
- Издательство: Plenum Publishers
- Местоположение издательства: United States
- Первая страница: 811
- Последняя страница: 839
- DOI: 10.1007/s10958-020-04655-x
- Аннотация: In practice, we often encounter situations where a sample size is not defined in advance andcan be a random value. In the present paper, we derive second-order Chebyshev–Edgeworth andCornish–Fisher expansions based of Student’s t- and Laplace distributions and their quantiles forsamples with random size of a special kind. This derivation uses a general transfer theorem, whichallows us to construct asymptotic expansions for distributions of randomly normalized statisticsfrom the distributions of the considered non-randomly normalized statistics and of the random sizeof the underlying sample. Recently, interest in Cornish–Fisher expansions has increased becauseof study in risk management. Widespread risk measure Value at Risk (VaR) substantially dependson quantiles of the loss function, which is connected with description of investment portfolio offinancial instruments. Bibliography: 22 titles.
- Добавил в систему: Ульянов Владимир Васильевич