Certainty bands for the conditional cumulative distribution function and applications

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

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

In this paper, we establish uniform asymptotic certainty bands for the conditional cumulative distribution function. To this aim, we give exact rate of strong uniform consistency for the local linear estimator of this function. The corollaries of this result are the asymptotic certainty bands for the quantiles and the regression function. We illustrate our results with simulations.

Mots clés: Conditional cumulative distribution function; local polynomial estimator; uniform asymptotic certainty bands; regression function; quantiles

Domaines: Statistiques [math.ST]

Aurélie Muller-Gueudin, Sandie Ferrigno, Myriam Maumy-Bertrand. Certainty bands for the conditional cumulative distribution function and applications. 47èmes Journées de Statistique de la SFdS, Jun 2015, Lille, France. ⟨hal-01154624v2⟩