题名

Bandwidth Selection for Kernel Quantile Estimation

DOI

10.29973/JCSA.200609.0004

作者

Ming-Yen Cheng；Shan Sun

关键词

Bandwidth ； kernel ； quantile ； nonparametric smoothing

期刊名称

中國統計學報

卷期/出版年月

44卷3期（2006 / 09 / 01）

页次

271 - 295

内容语文

英文
英文摘要

In this article, we summarize some quantile estimators and related bandwidth selection methods and give two new bandwidth selection methods. By four distributions: standard normal, exponential, double exponential and log normal we simulated the methods and compared their efficiencies to that of the empirical quantile. It turns out that kernel smoothed quantile estimators, with no matter which bandwidth selection method used, are more efficient than the empirical quantile estimator in most situations. And when sample size is relatively small, kernel smoothed estimators are especially more efficient than the empirical quantile estimator. However, no one method can beat any other methods for all distributions.
主题分类 基礎與應用科學 > 統計
参考文献
  1. Faulk, M.(1984).Relative deficiency of kernel type estimators of quantiles.Ann. Stat.,12,261-268.
  2. Jones, M. C.(1992).Estimating densities, quantile, quantile densities and density quantiles.Ann. Inst. Statist. Math.,44,721-727.
  3. Nadaraya, E. A.(1964).Some new estimates for distribution functions.Theory Probab. Appl.,9,497-500.
  4. Parzen, E.(1979).Nonparametric statistical data modeling.J. Amer. Stat. Assoc.,74,105-131.
  5. Ralescu, S. S.,Sun, S.(1993).Necessary and sufficient conditions for the asymptotic normality of perturbed sample quantiles.J. Statist. Plann. Inference,35,55-64.
  6. Read, R.R.(1972).The asymptotic inadmissibility of the sample distribution function.Ann. Math. Statist.,43,89-95.
  7. Shankar, B.(1998).An optimal choice of bandwidth for perturbed sample quantiles, master thesis.
  8. Sheather, S. J.,Marron, J. S.(1990).Kernel quantile estimators.J. Amer. Statist. Assoc.,85,410-416.
  9. Wand, M. P.,Jones, M. C.(1995).Kernel smoothing.London:Chapman and Hall.
  10. Yamato, H.(1973).Uniform convergence of an estimator of a distribution function.Bull. Math. Statist.,15,69-78.
  11. Yang, S. S.(1985).A smooth nonparametric estimation of a quantile function.J. Amer. Stat. Assoc.,80,1004-1011.
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