Bandwidth Selection for Kernel Estimates

  • Luc Devroye
  • Gábor Lugosi
Part of the Springer Series in Statistics book series (SSS)


This chapter is about the choice of the bandwidth (or smoothing factor) h ∈ (0, ∞) of the standard kernel estimate
$$ {f_{n,h}}(x) = \frac{1}{{n{h^d}}}\sum\limits_{i = 1}^n {K\left( {\frac{{x - {X_i}}}{h}} \right)} . $$


Kernel Estimate Bandwidth Selection Smoothing Factor Asymptotic Optimality General Kernel 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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§11.8. References

  1. L. Devroye, “Universal smoothing factor selection in density estimation: Theory and practice (with discussion),” Test, vol. 6, pp. 223–320, 1997.MathSciNetMATHCrossRefGoogle Scholar
  2. L. Devroye, L. Györfi, and G. Lugosi, A Probabilistic Theory of Pattern Recognition, Springer-Verlag, New York, 1996.MATHGoogle Scholar
  3. L. Devroye and G. Lugosi, “A universally acceptable smoothing factor for kernel density estimation,” Annals of Statistics, vol. 24, pp. 2499–2512, 1996.MathSciNetMATHCrossRefGoogle Scholar
  4. L. Devroye and G. Lugosi, “Non-asymptotic universal smoothing factors, kernel complexity and Yatracos classes,” Annals of Statistics, vol. 25, pp. 2626–2637, 1997.MathSciNetMATHCrossRefGoogle Scholar
  5. L. Devroye and C. S. Penrod, “Distribution-free lower bounds in density estimation,” Annals of Statistics, vol. 12, pp. 1250–1262, 1984.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Luc Devroye
    • 1
  • Gábor Lugosi
    • 2
  1. 1.Computer Science DepartmentMcGill UniversityMontrealCanada
  2. 2.Facultat de Ciencies EconomiquesUniversitat Pompeu FabraBarcelonaSpain

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