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Uniform-in-Bandwidth Functional Limit Laws

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.
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Submitted on : Friday, August 4, 2017 - 8:39:25 PM
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Paul Deheuvels, Sarah Ouadah. Uniform-in-Bandwidth Functional Limit Laws. Journal of Theoretical Probability, Springer, 2013, 26 (3), pp.697-721. ⟨10.1007/s10959-011-0376-1⟩. ⟨hal-01572166⟩



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