Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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THE UNIFORM CONSISTENCY OF THE SAMPLE KERNEL QUANTILE PROCESS

  • Bae, Jong-Sig (Department of Mathematics and Institute of Basic Science, Sung-Kyunkwan University) ;
  • Kim, Sung-Yeun (Department of Mathematics and Institute of Basic Science, Sung-Kyunkwan University)
  • Published : 2004.08.01
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Abstract

We obtain a kernel quantile process based on the kernel quantile estimator and prove the uniform consistency of the kernel quantile process by developing that of the usual sample quantile process. We apply our result to the classical kernel type processes.

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References

  1. J. Bae and S. Kim, The uniform law of large numbers for the Kaplan-Meier integral process, Bull. Austral. Math. Soc. 67 (2003), 459–465
  2. R. R. Bahadur, A note on quantiles in large samples, Ann. Math. Statist. 37 (1966), 577–580
  3. V. Fabian, and J. Hannan, Introduction to probability and mathematical sataistics, Wiley series in probability and mathematical sataistics. Wiely, New York, 1984
  4. M. Falk, Asymptotic normality of the kernel quantile estimator, Ann. Statist. 13 (1985), 428–433
  5. A. F. Karr, Probability, Springer-Verlag, New York, 1993
  6. E. Parzen, Nonparametric statistitical data modeling, J. Amer. Statist. Assoc. 74 (1979), 105–131
  7. S. J. Sheather and J. S. Marron, Kernel quantile estimators, J. Amer. Statist. Assoc. 85 (1990), 410–416
  8. S. S. Yang, A smooth nonparametric estimator of a quantile function, J. Amer. Statist. Assoc. 80 (1985), 1004–1011