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Teor. Veroyatnost. i Primenen., 2002, Volume 47, Issue 1, Pages 110–130 (Mi tvp3003)  

This article is cited in 1 scientific paper (total in 1 paper)

Test of symmetry in nonparametric regression

F. Leblanca, O. V. Lepskiĭb

a University of Grenoble 1 — Joseph Fourier
b Université de Provence

Abstract: The minimax properties of a test verifying a symmetry of an unknown regression function $f$ from $n$ independent observations are studied. The underlying design is assumed to be random and independent of the noise in observations. The function $f$ belongs to a ball in a Hölder space of regularity $\beta$. The null hypothesis accepts that $f$ is symmetric. We test this hypothesis versus the alternative that the $L_2$ distance from $f$ to the set of symmetric functions exceeds $\sqrt{r_n/2}$. As shown, these hypotheses can be tested consistently when $r_n=O(n^{-4\beta/(4\beta+1)})$.

Keywords: minimax hypothesis testing, minimax decision, Hölder class.

DOI: https://doi.org/10.4213/tvp3003

Full text: PDF file (1653 kB)

English version:
Theory of Probability and its Applications, 2003, 47:1, 34–52

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Received: 02.07.1999
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Citation: F. Leblanc, O. V. Lepskiǐ, “Test of symmetry in nonparametric regression”, Teor. Veroyatnost. i Primenen., 47:1 (2002), 110–130; Theory Probab. Appl., 47:1 (2003), 34–52

Citation in format AMSBIB
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\by F.~Leblanc, O.~V.~Lepski{\v\i}
\paper Test of symmetry in nonparametric regression
\jour Teor. Veroyatnost. i Primenen.
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\pages 110--130
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\zmath{https://zbmath.org/?q=an:1036.62036}
\transl
\jour Theory Probab. Appl.
\yr 2003
\vol 47
\issue 1
\pages 34--52
\crossref{https://doi.org/S0040585X97979482}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000183800400003}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Bissantz N., Holzmann H., Pawlak M., “Testing for Image Symmetries–with Application to Confocal Microscopy”, IEEE Transactions on Information Theory, 55:4 (2009), 1841–1855  crossref  mathscinet  zmath  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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