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Theory and Method

Comparison of Smoothing Parameterizations in Bivariate Kernel Density Estimation

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Pages 520-528 | Received 01 Apr 1991, Published online: 27 Feb 2012

References

  • Cacoullos , T. 1966 . Estimation of a Multivariate Density . Annals of the Institute of Statistical Mathematics , 18 : 179 – 189 .
  • Deheuvels , P. 1977 . Estimation Non Parametrique de la Densité par Histogrammes Generalises (II) . Publications de l'Institut Statistique de l'Université de Paris , 22 : 1 – 23 .
  • Epanechnikov , V. A. 1969 . Non-Parametric Estimation of a Multivariate Probability Density . Theory of Probability and Its Applications , 14 : 153 – 158 .
  • Fukunaga , K. 1972 . Introduction to Statistical Pattern Recognition , New York : Academic Press .
  • Hall , P. and Marron , J. S. 1988 . Variable Window Width Kernel Estimates of Probability Densities . Probability Theory and Related Fields , 80 : 37 – 49 .
  • Härdle , W. 1990a . Applied Nonparametric Regression , Cambridge , , UK : Cambridge University Press .
  • Härdle , W. 1990b . Smoothing Techniques With Implementation in S , New York : Springer-Verlag .
  • Marron , J. S. and Wand , M. P. 1992 . Exact Mean Integrated Squared Error . The Annals of Statistics , 20 : 712 – 736 .
  • Müller , H.-G. and Prewitt , K. A. 1991 . “ Applications of Multiparameter Weak Convergence for Adaptive Nonparametric Curve Estimation ” . In Nonparametric Functional Estimation and Related Topics , Edited by: Roussas , G. G. 141 – 166 . Dordrecht : Klüwer .
  • Rudin , W. 1973 . Functional Analysis , New York : McGraw-Hill .
  • Scott , D. W. 1985 . Average Shifted Histograms: Effective Nonparametric Density Estimators in Several Dimensions . The Annals of Statistics , 13 : 1024 – 1040 .
  • Scott , D. W. 1992 . Multivariate Density Estimation , New York : John Wiley .
  • Scott , D. W. and Wand , M. P. 1991 . Feasibility of Multivariate Density Estimates . Biometrika , 78 : 197 – 206 .
  • Sheather , S. J. and Jones , M. C. 1991 . A Reliable Data-Based Bandwidth Selection Method for Kernel Density Estimation . Journal of the Royal Statistical Society , 53 : 683 – 690 . Ser. B
  • Silverman , B. W. 1986 . Density Estimation for Statistics and Data Analysis , New York : Chapman and Hall .
  • Terrell , G. R. and Scott , D. W. 1992 . Variable Kernel Density Estimates . The Annals of Statistics , 20 : 1236 – 1265 .
  • Wand , M. P. 1992 . Error Analysis for General Multivariate Kernel Estimators . Journal of Nonparametric Statistics , 2 : 1 – 15 .
  • Wand , M. P. , Marron , J. S. and Ruppert , D. 1991 . Transformations in Density Estimation . Journal of the American Statistical Association , 86 : 343 – 361 . with comments

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