Uniform law of the logarithm for the conditional distribution function and application to certainty bands

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

1 BIGS - Biology, genetics and statistics
2 IRMA - Institut de Recherche Mathématique Avancée

In this paper, we establish exact rate of strong uniform consistency for the local linear estimator of the conditional distribution function. As a consequence of our main result, we give asymptotic uniform certainty bands. We illustrate our results with simulations.

Keywords: local polynomial estimator; Conditional distribution function; asymptotic uniform certainty bands

Domains: Statistics [math.ST]; Statistics Theory [stat.TH]

Sandie Ferrigno, Myriam Maumy-Bertrand, Aurélie Muller. Uniform law of the logarithm for the conditional distribution function and application to certainty bands. 2011. ⟨hal-00641027⟩