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Central limit theorems for local empirical processes near boundaries of sets

Einmahl,J.H.J.
; 
Khmaladze,E.V.
Abstract
We define the local empirical process, based on n i.i.d. random vectors in dimension d, in the neighborhood of the boundary of a fixed set. Under natural conditions on the shrinking neighborhood, we show that, for these local empirical processes, indexed by classes of sets that vary with n and satisfy certain conditions, an appropriately defined uniform central limit theorem holds. The concept of differentiation of sets in measure is very convenient for developing the results. Some examples and statistical applications are also presented.
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Appeared earlier as CentER Discussion Paper 2007-66
Date
2011
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Tilburg University Research Output Collection
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Einmahl, J H J & Khmaladze, E V 2011, 'Central limit theorems for local empirical processes near boundaries of sets', Bernoulli, vol. 17, no. 2, pp. 545-561. < http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?handle=euclid.bj/1302009236&view=body&content-type=pdfview_1 >
URI
https://hdl.handle.net/20.500.14602/53191
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