Uniform-in-bandwidth kernel estimation for censored data |
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Authors: | Sarah Ouadah |
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Affiliation: | L.S.T.A., Université Pierre et Marie Curie (Paris 6), T15-25, E2, 4 Place Jussieu, 75252 Paris Cedex 05, France |
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Abstract: | 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. |
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Keywords: | Functional limit laws Right random censorship model Kernel lifetime density estimators Kernel failure rate estimators Kaplan&ndash Meier empirical process Convergence in probability |
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