Abstract
Based on a uniform functional central limit theorem (FCLT) for unbiased smoothed empirical processes indexed by a class.F of measurable functions defined on a linear metric space we present a consistency theorem for smoothed bootstrapped empirical processes. Our approach and the results are comparable with those in Giné and Zinn [8], and Giné [10], respectively, in the case of empirical processes; especially, our Theorem 2.2 below is comparable with the main result stated as Theorem 2.3 in Giné and Zinn [8].
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Gaenssler, P., Rost, D. (2003). Smoothed Empirical Processes and the Bootstrap. In: Hoffmann-Jørgensen, J., Wellner, J.A., Marcus, M.B. (eds) High Dimensional Probability III. Progress in Probability, vol 55. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8059-6_18
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DOI: https://doi.org/10.1007/978-3-0348-8059-6_18
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