286
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

Adaptive normal reference bandwidth based on quantile for kernel density estimation

Pages 2869-2880 | Received 29 Nov 2010, Accepted 02 Mar 2011, Published online: 21 Apr 2011

References

  • Bowman , A. W. 1984 . An alternative method of cross-validation for the smoothing of density estimates . Biometrika , 71 : 353 – 360 .
  • Copas , J. P. and Fryer , M. J. 1980 . Density estimation and suicide risks in psychiatric treatment . J. R. Statist. Soc., Ser. B , 143 : 167 – 176 .
  • Devroye , L. and Györfi , L. 1985 . Nonparametric Density Estimation: The L 1 View , New York : John Wiley .
  • Hall , P. and Marron , J. S. 1991 . Local minima in cross-validation functions . J. R. Statist. Soc., Ser. B , 53 : 245 – 252 .
  • Hall , P. , Marron , J. S. and Park , B. U. 1992 . Smoothed cross validation . Probab. Theory Relat. Fields , 92 : 1 – 20 .
  • Härdle , W. 1991 . Smoothing Techniques with Implementation in S , New York : Springer .
  • Marron , J. S. and Wand , M. P. 1992 . Exact mean integrated squared error . Ann. Statist , 20 : 712 – 736 .
  • Parzen , E. 1962 . On estimation of a probability density function and mode . Ann. Math. Statist , 33 : 1065 – 1076 .
  • Rosenblatt , W. 1956 . Remarks on some nonparametric estimates of a density function . Ann. Math. Statist , 27 : 832 – 837 .
  • Rudemo , M. 1982 . Empirical choice of histograms and kernel density estimators . Scand. J. Statist , 9 : 65 – 78 .
  • Scott , W. D. 1992 . Multivariate Density Estimation: Theory, Practice, and Visualization , New York : Wiley .
  • Scott , D. W. and Terrell , G. R. 1987 . Biased and unbiased cross-validation in density estimation . J. Amer. Statist. Assoc , 82 : 1131 – 1146 .
  • Sheather , S. J. and Jones , M. C. 1991 . A reliable data-based bandwidth selection method for kernel density estimation . J. R. Statist. Soc., Ser. B , 53 : 683 – 690 .
  • Silverman , B. W. 1986 . Density Estimation for Statistics and Data Analysis , London : Chapman and Hall .
  • Simonoff , J. S. 1996 . Smoothing Methods in Statistics , New York : Springer-Verlag .
  • Stone , C. J. 1984 . An asymptotically optimal window selection rule for kernel density estimates . Ann. Statist , 12 : 1285 – 1297 .
  • Venables , W. N. and Ripley , B. D. 2002 . Modern Applied Statistics with S , 4 , New York : Springer .
  • Wand , M. P. and Jones , M. C. 1995 . Kernel Smoothing , London : Chapman and Hall .
  • Weisberg , S. 1980 . Applied Linear Regression , New York : Wiley .
  • Zhang , J. and Wang , X. 2009 . Robust normal reference bandwidth for kernel density estimation . Statist. Neerlandica , 63 : 13 – 23 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.