We consider the local maximum likelihood estimation of , unknown parameter of the conditional distribution of Y given . The aim of this Note is the study of strong uniform consistency rates of the local maximum likelihood kernel estimator. Under suitable regularity conditions, we establish a uniform law of the logarithm for the maximal deviation of this estimator. The method of proof is based upon functional limit laws derived by modern empirical process theory.
Nous considérons l'estimation par la méthode du maximum de vraisemblance local de , paramètre inconnu de la distribution conditionnelle de Y sachant . Le but de cette Note est d'étudier la vitesse de convergence uniforme presque sûre de l'estimateur à noyau du maximum de vraisemblance local. En s'appuyant sur la théorie moderne des processus empiriques indexés par des classes de fonctions, nous établissons une loi uniforme du logarithme concernant la déviation maximale de cet estimateur.
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David Blondin 1
@article{CRMATH_2006__342_3_207_0, author = {David Blondin}, title = {Vitesse de convergence presque s\^ure de l'estimateur \`a noyau du maximum de vraisemblance local}, journal = {Comptes Rendus. Math\'ematique}, pages = {207--210}, publisher = {Elsevier}, volume = {342}, number = {3}, year = {2006}, doi = {10.1016/j.crma.2005.12.011}, language = {fr}, }
David Blondin. Vitesse de convergence presque sûre de l'estimateur à noyau du maximum de vraisemblance local. Comptes Rendus. Mathématique, Volume 342 (2006) no. 3, pp. 207-210. doi : 10.1016/j.crma.2005.12.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.12.011/
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