Chung-type functional laws of the iterated logarithm for tail empirical processes
作者： P Deheuvels
DOI: 10.1016/S0246-0203(00)00143-6
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摘要: Abstract We obtain functional laws of the iterated logarithm for tail empirical process analogue to Chung (1948) and Csaki (1980) limit Wiener process. The is defined by hn−1/2αn(hnu) 0≤u≤1 , where αn denotes uniform based upon n independent (0,1) random variables. Under appropriate assumptions on hn→0 Mason (1988) showed that sequence functions fn=(2hnlog logn)−1/2αn(hn·) almost surely compact with respect topology sup-norm ‖·‖ gave a characterization corresponding set K . In this paper, we an estimate rate law evaluating lim inf n→∞ ( log n)‖f −f‖ each f∈
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