title: To the history of Saint-Petersburg school of Probability and Statistics. IV. Characterization of distributions and limit theorems in statistics.
metadata.name: dc.contributor.author
metadata.value: Zaitsev, Andrey Yu.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Kagan, Abram M.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Nikitin, Yakov Yu.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2019-05-24T08:22:11Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2019-05-24T08:22:11Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2019-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Zaitsev A.Yu., Kagan A. M., Nikitin Ya.Yu. To the history of Saint-Petersburg school of Probability and Statistics. IV. Characterization of distributions and limit theorems in statistics. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2019, vol. 6 (64), issue 1, pp. 53–80.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2019.104
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/15537
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: This is the fourth article in a series of surveys devoted to the scientiﬁc achievements of the Leningrad - Saint-Petersburg school of Probability and Statistics during the period from 1947 to 2017. It is devoted to the works on characterization of distributions and various limit theorems in Statistics including asymptotic eﬃciency of tests, criteria based on characterizations and normal approximation for L1 -norms of kernel density estimators. The characterization results are related to independence and equidistribution of linear and non-linear forms of the sample as well as to regression relations, admissibility and optimality of statistical estimators. When calculating the Bahadur eﬃciency, we give attention to the logarithmic asymptotics for large deviations of test statistics under the hypothesis. We study also the conditions of local asymptotic optimality in Bahadur sense for various nonparametric tests.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: Работа выполнена при частичной финансовой поддержке РФФИ (гранты № 16-01-00367 и 16-01-00258), гранта СПбГУ-ННИО 6.65.37.2017 и при поддержке программы Президиума РАН № 01 «Фундаментальная математика и ее приложения» (грант PRAS-18-01).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 6 (64); Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: characterization of distributions
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: regression
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: equidistribution
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: empirical process
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: kernel density estimators
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: large deviations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: asymptotic efficiency
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: U-statistics
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: normal approximation
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: To the history of Saint-Petersburg school of Probability and Statistics. IV. Characterization of distributions and limit theorems in statistics.
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 53-80.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/15537/1/53-80.pdf
resources.format: Adobe PDF
resources.size: 451,08 kB