title: On uniform consistency of Neyman’s type nonparametric tests
metadata.name: dc.contributor.author
metadata.value: Ermakov, Mikhail S.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Kapatsa, David Yu.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2023-05-18T21:40:24Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2023-05-18T21:40:24Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2023-05
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Ermakov M. S., Kapatsa D.Yu. On uniform consistency of Neyman’s type nonparametric tests. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2023, vol. 10 (68), issue 2, pp. 212–225. https://doi.org/10.21638/spbu01.2023.203 (In Russian)
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2023.203
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/41479
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The goodness-of-fit problem is explored, when the test statistic is a linear combination of
  squared Fourier coefficients’ estimates coming from the Fourier decomposition of a probability
  density. Common examples of such statistics include Neyman’s test statistics and test statistics, generated by L2-norms of kernel estimators. We prove the asymptotic normality
  of the test statistic for both the null and alternative hypothesis. Using these results
  we deduce conditions of uniform consistency for nonparametric sets of alternatives, which
  are defined in terms of distribution or density functions. Results on uniform consistency,
  related to the distribution functions, can be seen as a statement showing to what extent
  the distance method, based on a given test statistic, makes the hypothesis and alternatives
  distinguishable. In this case, the deduced conditions of uniform consistency are close
  to necessary. For sequences of alternatives — defined in terms of density functions — approaching
  the hypothesis in L2-metric, we find necessary and sufficient conditions for their
  consistency. This result is obtained in terms of the concept of maxisets, the description of
  which for given test statistics is found in this publication.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: This work was supported by the Russian Foundation for Basic Research (project no. 20-01-00273).
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 10; Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: nonparametric hypothesis testing
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: goodness of fit tests
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Neyman’s test
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: consistency
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: nonparametric set of alternatives
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: density hypothesis testing
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On uniform consistency of Neyman’s type nonparametric tests
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 212-225.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/41479/1/212-225.pdf
resources.format: Adobe PDF
resources.size: 365,66 kB