Acta mathematica scientia,Series B ›› 2003, Vol. 23 ›› Issue (2): 155-.

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A NOTE ON OSCILLATION MODULUS OF PL-PROCESS AND ITS APPLICATIONS UNDER RANDOM CENSORSHIP

 ZHOU Yong   

  1. Institute of Applied Mathematics, Academy of Mathematics and System Sciences,
    Chinese Academy of Science, Beijing100080, China
  • Online:2003-04-07 Published:2003-04-07
  • Supported by:

    Received March 10, 2000; revised March 10, 2002. This work was supported by Fund of National Natural
    Science (10171103) of China

Abstract:

The strong limit results of oscillation modulus of PL-process are established in
this paper when the density function is not continuous function for censored data. The rates
of convergence of oscillation modulus of PL-process are sharp under week condition. These
results can be used to derive laws of the iterated logarithm of random bandwidth kernel
estimator and nearest neighborhood estimator of density under continuous conditions of
density function being not assumed.

Key words: Product-limit (PL) estimator, censorship, random bandwidth, kernel estimator,nearest neighborhood estimator

CLC Number: 

  • 62G30
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