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The almost sure behavior of the oscillation modulus for PL-process and cumulative hazard process under random censorship

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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.

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Authors and Affiliations

  1. Institute of Applied Mathematics, Chinese Academy of Sciences, 100080, Beijing, China

    Zhou Yong & Sun Liuquan

  2. Department of Statistics, University of Hong Kong, Hong Kong, China

    Paul S. F. Yip

Authors
  1. Zhou Yong
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  2. Sun Liuquan
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  3. Paul S. F. Yip
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Additional information

Project supported in part by the National Natural Science Foundation of China (Grant No. 19701037).

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Yong, Z., Liuquan, S. & Yip, P.S.F. The almost sure behavior of the oscillation modulus for PL-process and cumulative hazard process under random censorship. Sci. China Ser. A-Math. 42, 225–237 (1999). https://doi.org/10.1007/BF02879056

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  • DOI: https://doi.org/10.1007/BF02879056

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