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Uniform law of the logarithm for the local linear estimator of the conditional distribution function

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Title: Uniform law of the logarithm for the local linear estimator of the conditional distribution function
Alternate Title: Loi uniforme du logarithme pour l'estimateur linéaire local de la fonction de répartition conditionnelle
Authors: Ferrigno, Sandie1 sandie.ferrigno@iecn.u-nancy.fr, Maumy-Bertrand, Myriam2 myriam.maumy@math.unistra.fr, Muller, Aurélie1 aurelie.muller@iecn.u-nancy.fr
Source: Comptes Rendus. Mathématique. Sep2010, Vol. 348 Issue 17/18, p1015-1019. 5p.
Subjects: Logarithms, Linear systems, Distribution (Probability theory), Parameter estimation, Mathematical analysis
Abstract (English): Abstract: In this Note, we first recall the results of the behaviour of the nonparametric estimator of the conditional distribution function which we can find in the literature. We establish exact rate of strong uniform consistency for the local linear estimator of the conditional distribution function. Our methods of proofs are based upon modern empirical process theory in the spirit of the results of Einmahl and Mason (2000) and Deheuvels and Mason (2004) . [ABSTRACT FROM AUTHOR]
Abstract (French): Résumé: Dans cette Note, nous rappelons d''''abord les résultats sur le comportement de l''''estimateur non paramétrique de la fonction de répartition conditionnelle, que nous pouvons trouver dans la littérature. Puis, nous établissons la vitesse exacte de la consistance forte uniforme pour l''''estimateur linéaire local de la fonction de répartition conditionnelle. Pour démontrer nos résultats, nous utiliserons les théories récentes faisant intervenir des processus tous dérivant du processus empirique dans l''''esprit des articles de Einmahl et Mason (2000) et de Deheuvels et Mason (2004) .
Copyright of Comptes Rendus. Mathématique is the property of Academie des Science, Centre Mersenne and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 53970633
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Uniform law of the logarithm for the local linear estimator of the conditional distribution function
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  Data: Loi uniforme du logarithme pour l'estimateur linéaire local de la fonction de répartition conditionnelle
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  Data: <searchLink fieldCode="JN" term="%22Comptes+Rendus%2E+Mathématique%22">Comptes Rendus. Mathématique</searchLink>. Sep2010, Vol. 348 Issue 17/18, p1015-1019. 5p.
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  Data: <searchLink fieldCode="DE" term="%22Logarithms%22">Logarithms</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+systems%22">Linear systems</searchLink><br /><searchLink fieldCode="DE" term="%22Distribution+%28Probability+theory%29%22">Distribution (Probability theory)</searchLink><br /><searchLink fieldCode="DE" term="%22Parameter+estimation%22">Parameter estimation</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+analysis%22">Mathematical analysis</searchLink>
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  Label: Abstract (English)
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  Data: Abstract: In this Note, we first recall the results of the behaviour of the nonparametric estimator of the conditional distribution function which we can find in the literature. We establish exact rate of strong uniform consistency for the local linear estimator of the conditional distribution function. Our methods of proofs are based upon modern empirical process theory in the spirit of the results of Einmahl and Mason (2000) and Deheuvels and Mason (2004) . [ABSTRACT FROM AUTHOR]
– Name: Abstract
  Label: Abstract (French)
  Group: Ab
  Data: Résumé: Dans cette Note, nous rappelons d''''abord les résultats sur le comportement de l''''estimateur non paramétrique de la fonction de répartition conditionnelle, que nous pouvons trouver dans la littérature. Puis, nous établissons la vitesse exacte de la consistance forte uniforme pour l''''estimateur linéaire local de la fonction de répartition conditionnelle. Pour démontrer nos résultats, nous utiliserons les théories récentes faisant intervenir des processus tous dérivant du processus empirique dans l''''esprit des articles de Einmahl et Mason (2000) et de Deheuvels et Mason (2004) . </ce:abst [Copyright 2010 Elsevier]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Comptes Rendus. Mathématique is the property of Academie des Science, Centre Mersenne and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.crma.2010.08.003
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        Text: English
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        PageCount: 5
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      – SubjectFull: Logarithms
        Type: general
      – SubjectFull: Linear systems
        Type: general
      – SubjectFull: Distribution (Probability theory)
        Type: general
      – SubjectFull: Parameter estimation
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      – SubjectFull: Mathematical analysis
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      – TitleFull: Uniform law of the logarithm for the local linear estimator of the conditional distribution function
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            NameFull: Ferrigno, Sandie
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            NameFull: Maumy-Bertrand, Myriam
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            NameFull: Muller, Aurélie
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              M: 09
              Text: Sep2010
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              Y: 2010
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              Value: 17/18
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