Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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ASYMPTOTIC APPROXIMATION OF KERNEL-TYPE ESTIMATORS WITH ITS APPLICATION

  • Kim, Sung-Kyun (Department of Computer Engineering, Myongji University) ;
  • Kim, Sung-Lai (Department of Mathematics, Chungnam National University) ;
  • Jang, Yu-Seon (Department of mathematics, Chungnan National University)
  • Published : 2004.05.01

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Abstract

Sufficient conditions are given under which a generalized class of kernel-type estimators allows asymptotic approximation on the modulus of continuity. This generalized class includes sample distribution function, kernel-type estimator of density function, and an estimator that may apply to the censored case. In addition, an application is given to asymptotic normality of recursive density estimators of density function at an unknown point.

Keywords

References

  1. Ann. Math. Statist. v.37 A note on quantiles in large samples R.R. Bahadur
  2. Sequential Analysis v.8 no.2 Berry-Esseen type theorems for sequential density estimation A.K. Basu;D.K. Sahoo
  3. Z. Wahrscheinlichkeitstheorie verw. Gebiete v.36 On sequential density estimation R.J. Carroll
  4. Sankya Ser. A v.46 On almost sure representations for quantiles of the product-limit estimator with applications K.G. Cheng
  5. Cornmun. Statist-Theory Meth. v.22 no.11 Asymptotic properties of quantiles for truncated and contaminated data F. Dong
  6. J. Statist. Plann. Inference v.18 Weak asymptotic representations for quantiles of the product-limit estimator I. Gijbels;N. Veraverbeke
  7. J. Statist. Plann. Inference v.22 Sequential fixed-width confidence intervals for quantiles in the presence of censoring I. Gijbels;N. Veraverbeke
  8. Journal of the Korean Statistical Society v.28 Sequential confidence intervals for quantiles based on recursive density estimators S.K. Kim;S.L. Kim
  9. Korean J. of Comput. & Appi. Math. v.8 Asymptotic properties of random central order statistics under contamination S.K. Kim and S.L. Kim
  10. Nonparametric Functional Estimation B.L.S. Prakasa Rao
  11. Approximation Theorems of Mathematical Statistics R.J. Serfling