The almost sure behavior of the oscillation modulus for PL-process and cumulative hazard process under random censorship |
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| Authors: | Zhou Yong Sun Liuquan Paul S F Yip |
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| Institution: | (1) Institute of Applied Mathematics, Chinese Academy of Sciences, 100080 Beijing, China;(2) Department of Statistics, University of Hong Kong, Hong Kong, China |
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| Abstract: | The local behavior of oscillation modulus of the product-limit (PL) process and the cumulative hazard process is investigated
when the data are subjected to random censoring. Laws of the iterated logarithm of local oscillation modulus for the PL-process
and the cumulative hazard process are established. Some of these results are applied to obtain the almost sure best rates
of convergence for various types of density estimators as well as the Bahadur-Kiefer type process.
Project supported in part by the National Natural Science Foundation of China (Grant No. 19701037). |
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| Keywords: | censorship oscillation modulus product-limit process cumulative hazard process law of the iterated logarithm (LIL) |
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