Abstract
We present functional central limit theorems (FCLT) for smoothed empirical processes indexed by a class F of measurable functions defined on a linear metric space X via the random measure process (RMP) approach. We shall work under rather weak conditions and shall e.g. not need the rather restrictive assumption of F being invariant under translation. The results should be compared to those obtained by van der Vaart (1994) and Yukich (1992) who tackled the problem from a different angle.
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Rost, D. (2000). Limit Theorems for Smoothed Empirical Processes. In: Giné, E., Mason, D.M., Wellner, J.A. (eds) High Dimensional Probability II. Progress in Probability, vol 47. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1358-1_8
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DOI: https://doi.org/10.1007/978-1-4612-1358-1_8
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