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Original Articles

Convergence rates for average square errors for kernel smoothing estimators

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Pages 209-228 | Published online: 12 Apr 2007

References

  • Devroye and Gyofri . 1985 . Nonparametric density estimation: the L1 view , New York : John Wiley .
  • Fan , J. 1993 . Local linear regression smoothers and their minimax efficiencies . Annals of Statistics , 21 : 196 – 216 .
  • Grund , B. , Hall , P. and Marron , J. S. 1994 . Loss and risk in smoothing parameter selection . Journal of Nonparametric Statistics , 4 : 107 – 132 .
  • Hall , P. 1984a . Central limit theorem for integrated square error of multivariate nonparametric density estimation . Journal of Multivariae Analysis , 14 : 1 – 16 .
  • Hall , P. 1984b . Integrated square error properties of kernel estimators of regression function . Annals of Statistics , 12 : 241 – 260 .
  • Hall , P. and Marron , J. S. 1987 . Extent to which least-squares cross validation minimizes integrated square error in nonparametric density estimation . Probability Theory and its Related Fields , 74 : 567 – 581 .
  • Härdle , W. , Hall , P. and Marron , J. S. 1988 . How far are automatically chosen regression smoothing parameters from their optimum? . Journal of the American Statistical Association , 83 : 86 – 95 .
  • Härdle , W. and Marron , J. S. 1985 . Optimal bandwidth selection rule in nonparametric regression . Ann. Statist , 13 : 1465 – 1481 .
  • Jones , M. C. , Marron , J. S. and Sheather , S. J. 1996 . A brief survey of bandwidth selection for density estimation . Journal of American Statistical Association , 91 : 401 – 407 .
  • Kim , T. Y. 1997 . Central limit theorems for quadratic errors of nonparametric estimators . Journal of Statistical Planning and Inference , 64 : 193 – 204 .
  • Kim , T. Y. and Cox , D. D. 1995 . Asymptotic behavior of some measures of accuracy in nonparametric curve estimation with dependent observations . Journal of Multi-variate Analysis , 53 : 67 – 93 .
  • Marron , J. S. 1987 . A comparison of cross validation techniques in density estimation . Annals of Statistics , 15 : 152 – 162 .
  • Marron , J. S. and Härdle , W. 1986 . Random approximation to some measures of accuracy in nonparametric curve estimation . Journal of Multivariate Analysis , 20 : 91 – 113 .
  • Marron and Tsybakov . 1995 . Visual Error Criteria for qualitative smoothing . Journal of the American Statistical Association , 90 : 499 – 507 .
  • Sain , S. R. , Baggcrly , K. A. and Scott , D. W. 1995 . Cross-validation of multivariate densities . Journal of the American Statistical Association , 89 : 807 – 817 .

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