Uniform-in-Bandwidth Functional Limit Laws

Paul Deheuvels () and Sarah Ouadah ()
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Paul Deheuvels: Université Pierre et Marie Curie (Paris 6)
Sarah Ouadah: Université Pierre et Marie Curie (Paris 6)

Journal of Theoretical Probability, 2013, vol. 26, issue 3, 697-721

Abstract: Abstract We provide uniform-in-bandwidth functional limit laws for the increments of the empirical and quantile processes. Our theorems, established in the framework of convergence in probability, imply new sharp uniform-in-bandwidth limit laws for functional estimators. In particular, they yield the explicit value of the asymptotic limiting constant for the uniform-in-bandwidth sup-norm of the random error of kernel density estimators. We allow the bandwidth to vary within the complete range for which the estimators are consistent.

Keywords: Functional limit laws; Kernel density estimators; Nonparametric functional estimators; Convergence in probability; Weak laws; Laws of large numbers; 62G05; 62G07; 62G20; 62G30; 60F15; 60F17 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10959-011-0376-1

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