Uniform-in-bandwidth kernel estimation for censored data

Sarah Ouadah (1)

1 LSTA - Laboratoire de Statistique Théorique et Appliquée

We present a sharp uniform-in-bandwidth functional limit law for the increments of the Kaplan-Meier empirical process based upon right-censored random data. We apply this result to obtain limit laws for nonparametric kernel estimators of local functionals of lifetime densities, which are uniform with respect to the choices of bandwidth and kernel. These are established in the framework of convergence in probability, and we allow the bandwidth to vary within the complete range for which the estimators are consistent. We provide explicit values for the asymptotic limiting constant for the sup-norm of the estimation random error

Mots clés: Functional limit laws; nonparametric kernel density estimation; right censorship model; kernel lifetime density estimators; kernel failure rate estimators; Kaplan-Meier empirical process; uniform empirical process; convergence in probability.; convergence in probability

Domaines: Théorie [stat.TH]

Sarah Ouadah. Uniform-in-bandwidth kernel estimation for censored data. 2012. ⟨hal-00766349⟩