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

Sandie Ferrigno (1, 2) , Myriam Maumy-Bertrand (3) , Aurélie Muller (1, 2)

1 IECN - Institut Élie Cartan de Nancy
2 BIGS - Biology, genetics and statistics
3 IRMA - Institut de Recherche Mathématique Avancée

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).

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Sandie Ferrigno, Myriam Maumy-Bertrand, Aurélie Muller. Uniform law of the logarithm for the local linear estimator of the conditional distribution function. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2010, 348 (17-18), pp.1015-1019. ⟨10.1016/j.crma.2010.08.003⟩. ⟨hal-00589788⟩