Certainty bands for the conditional cumulative distribution function and applications

Sandie Ferrigno (1, 2) , Bernard Foliguet (3) , Myriam Maumy-Bertrand (4) , Aurélie Muller-Gueudin (1, 2)

1 BIGS - Biology, genetics and statistics
2 IECL - Institut Élie Cartan de Lorraine
3 Service de Foetopathologie et placentologie [CHRU Nancy]
4 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 and an application on fetopathologic data.

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

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

Sandie Ferrigno, Bernard Foliguet, Myriam Maumy-Bertrand, Aurélie Muller-Gueudin. Certainty bands for the conditional cumulative distribution function and applications. 2014. ⟨hal-01025443⟩