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Uniform limit theorems under length-biased sampling and type I censoring. (English) Zbl 1488.60042

Summary: In recent years, in view of theory of empirical processes, authors have become more interested in the uniform analogue of the three fundamental theorems: the uniform law of large numbers of Glivenko-Cantelli type, the uniform central limit theorem for Donsker type and the functional law of the iterated logarithm (LIL). In this paper, under the bracketing entropy conditions, the uniform law of large numbers, uniform central limit theorem and the uniform LIL of Strassen type have been investigated in the case of length-biased and type I censoring.

MSC:

60F05 Central limit and other weak theorems
60F15 Strong limit theorems
60F17 Functional limit theorems; invariance principles
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