Bibliographic Details
| 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) .
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| Database: |
Engineering Source |
